# Geometry articles, theorems, problems

### What Is Geometry?

What Is Analytic Geometry?

Pictorial Geometry Index

- 1 + 27 = 12 + 16 Sangaku
- 120° Breeds 90° [Java]
- 3-4-5, Golden Ratio
- 3 Roads, 3 Travelers [Java]
- 3 Utilities Puzzle
- 3D Concurrency Of Altitudes
- Concurrence of the Altitudes As Seen from 3D [Java, GeoGebra]

- 3D Quadrilateral - a Coffin Problem
- 3-4-5 Triangle by a Kid
- 4 Travelers problem
- 5-Step Construction of the Golden Ratio, One of Many
- 5x5 Square Grid and 5 Circes [Java, GeoGebra]
- Puzzle of 25 Grid Points and 5 Circles [JavaScript, GeoGebra]
- Puzzle of 30 Grid Points and 5 Circles [JavaScript, GeoGebra]

- 6 to 9 Point Circle [Java]
- 60° Angle And Importance of Being The Other End of a Diameter
- 60
^{o}Breeds 90^{o}[Java] - 7 = 2 + 5 Sangaku
- 9-point Circle as a Locus of Concurrency [Java]
- 9 Point Center on Angle Bisector [GeoGebra]
- A 60° Rhombus in a 60° Isosceles Trapezoid
- A better solution to a difficult sangaku problem
- A Case of Similarity [Java]
- A Chain of Touching Circles in a Polygon (a la Bui Quang Tuan) [Java]
- A Chain of Touching Circles in a Polygon (à la Evelyn) [Java]
- A Characterization of the Euler Line [Java]
- A Circle in an Isosceles triangle from the 2006 Irish MO
- A Circle Related to Incenter and Circumcenter [Java]
- A Circle Rolling in an Equilateral Triangle [Java]
- A Circle With Two Centers [Java]
- A Conic in a Triangle [JavaScript, GeoGebra]
- A Combinaton Locus
- A Corrected Version of the Calculus Proof of the Pythagorean Theorem
- A Curious Identity in Triangle
- A Cyclic Inequality in Triangle
- A Cyclic Inequality in Triangle II
- A Cyclic Inequality in Triangle for Integer Powers
- A Degenerate Case of Bottema's Configuration [Java, GeoGebra]
- A Diameter As a Diagonal of Inscribed Quadrilateral [Java, GeoGebra]
- A Discovery of Hirotaka Ebisui And Thanos Kalogerakis
- A dissection puzzle. Proof #99 of the Pythagorean theorem
- A Double Meaning of an Arc's Midpoint [Java, GeoGebra]
- A Family of Cyclic Quadrilaterals [JavaScript, GeoGebra]
- A Generalization of Simson Line [JavaScript, GeoGebra]
- A Generalization of the Pythagorean Theorem
- A Generalization of Van Aubel's Theorem
- A Generalized Cavalieri-Zu Principle
- A Geometric Limit
- A Geometry Problem from 2012 IMO - Problem 5
- A Hard but Important Sangaku
- A Hinged Realization of a Plane Tessellation [Java]
- A Lemma of Equal Areas [Java]
- A Lemma on the Road to Sawayama
- A Line in a Square Grid [Java]
- A Line in Triangle Through the Circumcenter [Java]
- A Matter of Collinearity: Metamorphosis of a Problem
- A Modified Sangaku
- A Multiplicative Identity of Areas in a Triangle [Java]
- A Note on Cavalieri's Indivisibles
- A Parallelogram in Triangle [Java]
- A Plane Filling Curve for the Year 2017
- A Possibly First Proof of the Concurrence of Altitudes
- A Problem from Greece via Peru
- A Problem from the 1985 Balkan Mathematical Olympiad (Shortlist)
- A Problem in a Configuration of Three Squares
- A Problem in a Special Tangential Quadrilateral
- A Problem In an Isosceles Right Triangle [Java]
- A Problem in Pentagon with Right Angles
- A Problem in Pentagon with Supplementary Angles
- A Problem in Three Pentagons [JavaScript, GeoGebra]
- A Problem of Acute Triangle
- A Problem of Two Incircles by Miguel Ochoa Sanchez
- A Problem on an Icy Cone
- A problem with equilateral triangles [Java]
- A Problem with Right Isosceles Triangles [JavaScript]
- A Problem with Three Equilateral Triangles
- A Problem with Two Isosceles Triangles [JavaScript]
- A Problem with Two Similar Rectangles
- A Proof Perigal and All Others After Him Missed
- A Property of a Median [JavaScript, GeoGebra]
- A Property of Angle Bisectors
- A Property of Circle Through the Incenter [JavaScript]
- Another Property of Circle Through the Incenter [JavaScript]

- A Property of Incenter Relative to Circumcircle
- A Property of Cyclic Quadrilateral
- A Property of Equiangular Polygons [Java]
- A Property of Inscriptible Quadrilaterals [JavaScript]
- A Property of Isogonal Lines [JavaScript, GeoGebra]
- A Property of Orthic Triangle [JavaScript, GeoGebra]
- A Property of Pascal's Hexagon Pascal May Have Overlooked
- A Property of Perspective Triangles [JavaScript, GeoGebra]
- A Property of Points on Excircle
- A Property of Points on Incircle
- A Property of Rhombi [Java]
- A Property of the Line IO [Java]
- A Property of the Line IO: A Bundled Statement and Proof [Java]
- A Property of the Line IO: a proof from the Book [Java]
- A Property of Trapezoid with a Right Angle
- A Rectangle in Three Circles by Hirotaka Ebisui
- A Relation in Inscribed Tetrahedra
- A Relation in Triangle
- A Restored Sangaku
- A Sangaku Follow-Up on an Archimedes' Lemma [Java]
- A Sangaku: Two Unrelated Circles [Java]
- A Sangaku with an Egyptian Attachment [Java]
- A Sangaku with Many Circles and Some [Java]
- A Simple Solution to a Difficult Sangaku Problem
- A Special Point: Intersection of the Diagonals in Quadrilateral
- A Special Triangle with a Line Through the Lemoine Point
- A square in parallel lines
- A Straightedge Construction of the Midpoint of a Chord Common to Two Circles
- A Stronger Triangle Inequality [Java]
- A Sushi Morsel
- A Theorem of M. Mansion
- A Three Pegs Question [Java]
- A Triangle in a Rhombus with a 60 Degrees Angle
- A Triangle of Antreas Hatzipolakis [Java]
- A Triangle Problem from Caucasus
- A Triangle With a 45 Degrees Angle in Square
- A Trigonometric Identity in a Right Triangle from the 1960 IMO
- A Trigonometric Solution to a Difficult Sangaku Problem
- A Two-Triangle Inequality
- A Two-Triangle Inequality II
- A View on the Circle of Apollonius [JavaScript,GeoGebra]
- About a Line and a Triangle [Java]
- Abul Wafa al-Buzjani's Proof of the Pythagorean Theorem [Java]
- Abutting Equilateral Triangles on a Line I [JavaScript, GeoGebra]
- Acute Angle Bisectors in a Right Triangle [Java]
- Adams' Circle [Java]
- Addition and Subtraction Formulas for Sine and Cosine
- Addition and Subtraction Formulas for Sine and Cosine II
- Adil Abdulayev's Inequality With Angles, Medians, Inradius and Circumradius
- Adil Abdullayev's Inequality With Roots and Powers
- Algebraic proof of the theorem of butterflies in quadrilaterals
- Algebraic-Geometric Equation
- All about altitudes
- All Triangles Are Isosceles [Java]
- All Trigonometric Inequality in Triangle
- Altitudes and the Euler Line [GeoGebra]
- Altitudes and the Power of a Point [Java]
- Altitudes Concur at a Point: a Second Look
- Altitudes have ears, foot, stem, and root
- An Affine Property of Barycenter
- An Algebraic Lemma with Geometric Consequences [JavaScript]
- An All-Inclusive Inequality
- An All-Inclusive Inequality II
- An Angle in Square Conjoint with Regular Pentagon
- An Angle Inequality in Simple Polygons
- An Equilateral Triangle In Parallel Lines
- An Area Inequality
- An Area Inequality in Right Triangle
- An Asymmetric Inequality
- An Euclidean Construction with Inversion [Java, GeoGebra]
- An Extension of a Sangaku with Touching Circles
- An Extension of van Schooten's Theorem
- An Extra Triple of Equilateral Triangles for Napoleon [JavaScript, GeoGebra]
- An Identity for Regular Tetrahedra
- An Identity in a Regular Heptagon
- An Identity in (Cyclic) Quadrilaterals [JavaScript, GeoGebra]
- An Identity in Cyclic Quadrilateral
- An Identity in Triangle
- An Identity in Triangle II
- An Identity in Triangle with a 135 Degrees Angle
- An Inequality in Triangle with a Constraint
- An Inequality in Triangle with Side Lengths and Circumradius
- An Inequality with Exradii and an Altitude
- An Identity with Inradius and Circumradii
- An Inequality for Sides and Area
- An Inequality for the Cevians through Circumcenter
- An Inequality for the Cevians through Spieker Point via Brocard Angle
- An Inequality from the 2015 Romanian TST
- A Cyclic Inequality from the 6th IMO, 1964
- A Property of Nagel Cevians
- An Inequality in Acute Triangle, Courtesy of Ceva's Theorem
- An Inequality in Cyclic Quadrilateral
- An Inequality in Cyclic Quadrilateral II
- An Inequality in Cyclic Quadrilateral III
- An Inequality in Cyclic Quadrilateral IV
- An Inequality of the Areas of Triangles Formed by Circumcenter And Orthocenter
- An Inequality on Circumscribed Quadrilateral
- An Inequality in Triangle
- An Inequality in Triangle II
- An Inequality in Triangle III
- An Inequality in Triangle IV
- An Inequality in Triangle, V
- An Inequality in Triangle, VI
- An Inequality in Triangle XI
- An Inequality in Triangle, Mostly with the Medians
- An Inequality In Triangle That Involves the Four Basic Centers
- An Inequality in Triangle with Altitudes, Medians And Symmedians
- An Inequality in Triangle, with Integrals
- An Inequality in Triangle with Roots and Circumradius
- An Inequality in Triangle, with Sines
- An Inequality in Triangle, with Sines II
- An Inequality in Triangle with the Circumradius, Inradius and Angle Bisectors
- An Inequality in Triangle with the Sines of Half-Angles and Cube Roots
- An Inequality Involving Fermat Point
- An Inequality Not in Triangle
- An Inequality of Degree 3 with Inradius
- An Inequality with Altitudes and Angle Bisectors
- An Inequality with Altitudes and Medians
- An Inequality with Arctangents in Triangle
- An Inequality with Circumradii And Distances to the Vertices
- An inequality with Cosines and a Sine
- An Inequality with Inradius and Side Lengths
- An Inequality with Cotangents And the Circumradius
- An Inequality with Tangents and Sides
- An Inequality with One Tangent and Six Sines
- An inequality with Three Points
- An Inequality in Triangle with Differences of the Medians
- An Inequality with Inradius and Circumradii
- An Inequality in Triangle with the Medians, Sines and Cube Roots
- An Inequality with Powers of Six
- An Inequality with Sides, Altitudes, Angle Bisectors and Medians
- An Inequality with Sides, Cosines, and Semiperimeter
- An Inequality with Sin, Cos, Tan, Cot, and Some
- An Inequality with Sines
- An Inequality with Tangents and Cotangents
- An Inequality with the Most Important Cevians
- An Inradii Relation in Inscriptible Quadrilateral [JavaScript]
- An Isoperimetric Problem in Quadrilateral
- An Isoperimetric Theorem [Java]
- An Old Japanese Theorem
- An Unexpected Pair of Similar Triangles Which Are Equal [JavaScript, GeoGebra]
- An Unexpected Rhombus [JavaScript, GeoGebra]
- An Universal Inequality for Cevians
- An Unusual Generalization of the Pythagorean Theorem
- An Unusual Generalization of the Pythagorean Theorem, a Variant
- Angle: An Illustrated Classification [Java]
- Angle Bisector in Square
- Angle Bisectors Cross Circumcircle
- Angle Bisector in Equilateral Trapezoid
- Angle Bisector in Parallelogram [Java]
- Angle Bisectors In Rectangle [Java]
- Angle Bisector in Touching Circles [Java]
- Angle Bisectors [Java]
- Angle Bisectors and Perpendiculars in a Quadrilateral [Java]
- Angle Bisectors in Ellipse [Java]
- Angle Bisectors in Ellipse II [Java]
- Angle Bisectors in a Quadrilateral [Java]
- Angle Bisectors in a Quadrilateral - Cyclic and Otherwise [Java]
- Angle Bisectors On Circumcircle [Java]
- Angle Chasing on Radical Axis [JacaScritp, GeoGebra]
- Angle Chasing in a 75-30-75 triangle
- Angle in Square
- Angle in Right Triangle
- An Angle Inequality in Triangle with Perpendicular Medians
- Angle Preservation Property [Java]
- Angle Subtended by a Diameter [Java]
- Angle Trisection, the Impossibility of Thereof
- Angle Trisection by Archimedes [Java]
- Angle Trisection by Hippocrates [Java]
- Angle Trisection by Paul Vjecsner [Java]
- Angle Trisectors on Circumcircle [Java]
- Angle Trisection by Paper Folding
- Angles in 4-5-6 Triangle [JavaScript]
- Angles in a Cube I [Java]
- Angles in a Cube II [Java]
- Angles in a Cube III [Java]
- Angles in Triangle Add to 180
^{o} - Angles in a Triangle: an Exercise
- Angles Inscribed in an Absent Circle [Java]
- Another Concurrence on the 9-Point Circle [JavaScript, GeoGebra]
- Another Equilateral Triangle in Napoleon's Configuration [JavaScript, GeoGebra]
- Another Geometry Problem from 2012 IMO - Problem 1
- Another Golden Ratio in Semicircle
- Another Identity in Triangle
- Another Pair of Archimedean Twins - a Redux [JavaScript, GeoGebra]
- Another Property of Points on Incircle
- Another Property of the 9-Point Circle [JavaScript, GeoGebra]
- Another Refinement of the Ionescu-Weitzenbock Inequality
- Another Sangaku in Square
- Another Seven Circles Theorem [JavaScript, GeoGebra]
- Anticenter and Orthocenters [JavaScript, GeoGebra]
- Anticomplementary Triangle Surprise [Java]
- Antiparallel [Java]
- Antiparallel and Circumradius [JavaSCript, GeoGebra]
- Antiparallel via Three Reflections [Java]
- APMO 1995 Problem 3
- APMO 1998, Problem 4
- APMO 2002, Problem 3
- APMO 2003, Problem 2
- APMO 2004, Problem 2
- The Averages of Sides and Angles in a Triangle
- The Problem of Apollonius
- Apollonius Problem [Java]
- Apollonian Circle for Two Lines and a Circle [Java, GeoGebra]
- Apollonian Circles Theorem [Java]
- Apollonian Gasket [Java]
- CCC: Apollonius' Problem with Three Intersecting Circles [Java, GeoGebra]
- CCC: Gergonnes's Solution to Apollonius' Problem [Java, GeoGebra]
- Gergonne's Apollonian Circles

- Approximate Construction of Regular Pentagon by A. Dürer
- Arbelos -- the Shoemaker's Knife [Java]
- Another Pair of Twins in an Arbelos [Java]
- Archimedes' Quadruplets [Java]
- Archimedes' Twin Circles and a Brother [Java]
- Area and Perimeter of Circle
- Area Inequalities in Triangle
- Area Inequality in Three Triangles
- Area of an Arbelos [Java]
- Area of Cevian Triangle
- Area of Cutoff Triangles
- Area of Rectangle
- Area of the Intersection of Two Equal Rectangles [JavaScript, GeoGebra]
- Area of Trapezoid
- Area Optimization in Trapezoid
- Area, Sector Area, and Segment Area of an Ellipse
- Areas between Two Parallelograms [JavaScript, GeoGebra]
- Areas in Three Squares [JavaScript, GeoGebra]
- Average Distance to N Points
- Chain of Circles on a Chord [Java]
- Chain of Four Intersecting Circles [JavaScript, GeoGebra]
- Chain of Inscribed Circles [Java]
- Chain of Six Intersecting Circles [JavaScript, GeoGebra]
- Characterization of the Symmedian Point with Medians and Orthic Triangle
- Characterization of Trapezoid [JavaScript, GeoGebra]
- Chasing Secant Angles [JavaScript]
- Concurrence in Arbelos [JavaScript, GeoGebra]
- Concurrency in Arbelos [Java]
- Concurrence on Angle Bisector [JavaScript, GeoGebra]
- Concurrent Chords in a Circle, Equally Inclined
- Concyclic Points in Arbelos [Java]
- Rectangle in Arbelos [Java]
- Rectangular Areas in Circle [JavaScript, GeoGebra]
- Red and Pink Areas
- Reuleaux's Triangle, Extended [GeoGebra]
- Small Triangle from Small Triangle
- Square, 45 Degrees Angle and Pythagoras' Look-alike
- Square, Semicircle, and Other Curves [JavaScript, GeoGebra]
- Squares in Arbelos [Java]
- Twin Segments in Arbelos [Java]
- Archimedean Siblings out of Wedlock, i.e., Arbelos (JavaScript, GeoGebra)
- Archimedes'
*Book of Lemmas* - Arbelos' Morsels [JavaScript, GeoGebra]
- Book of Lemmas: Proposition 1 [Java]
- Book of Lemmas: Proposition 2 [Java]
- Book of Lemmas: Proposition 3 [Java]
- Book of Lemmas: Proposition 5 [Java]
- Book of Lemmas: Proposition 6 [Java]
- Book of Lemmas: Proposition 7
- Book of Lemmas: Proposition 9 [Java]
- Book of Lemmas: Proposition 10 [Java]
- Book of Lemmas: Proposition 11
- Book of Lemmas: Proposition 12 [Java]
- Book of Lemmas: Proposition 13 [Java]
- Book of Lemmas: Proposition 15

- Archimedes' Law of the Lever [Java]
- Archimedes' Method
- Archimedes' Twins in the Edo Period
- Area and Perimeter Splitters in a Triangle
- Area Inequality in Trapezoid
- Area Inequality in Triangle
- Area Inequality in Triangle II
- Area of a Bicentric Quadrilateral
- Area of a Circle by Leonardo da Vinci [Java]
- Area of a Circle by Rabbi Abraham bar Hiyya Hanasi [Java]
- Area of Isosceles Triangle
- Area of Median Triangle [Java]
- Area of Parallelogram [Java]
- Area of Parallelogram Formula by Shearing
- Area of the Union of Two Squares [Java]
- Area of Triangle [Java]
- Areas and Centroid in a Triangle [Java]
- Areas In Circle
- Areas in Square by Dissection [Java]
- Areas in Two Parallelograms and a Translation [JavaScript, GeoGebra]
- Arithmetic-Geometric Mean Inequality
- Arithmetic Mean Sangaku [Java]
- Arithmetic Mean Sangaku II [Java]
- Around the Incircle [Java]
- Around the Incircle in a Polygon [Java]
- Artisans vs Mathematicians
- Asian Pacific Kite [Java]
- Assigning Numbers to Points in the Plane
- Assimilation Illusion [Java]
- Asymmetric Propeller [Java]
- Asymmetric Propeller, the XXI Century
- Asymmetric Propeller by Plane Tiling [Java]
- A Final Chapter of the Asymmetric Propeller Story [JavaScript, GeoGebra]

- Axis of Similitude of Three Circles
- Barbier, The Theorem of [Java]
- Barycenter of Cevian Triangle
- Barycentric coordinates
- Batman's Problem [JavaScript, GeoGebra]
- Bender: A Visual Illusion [Java]
- Bespectacled Eyeballs Extension [JavaSCript, GeoGebra]
- Between a Cross and a Square (lies a Golden Ratio)
- Between Major and Minor Circles [Java]
- Bevan's Point and Theorem [Java]
- Beyond Pythagoras
- Beyond Viviani [JavaScript]
- Bimedians and Diagonals in a Quadrilateral
- Bimedians in a Regular Tetrahedron [Java]
- Bisectal Circle [Java]
- Bisecting arcs
- Bisecting a shape
- Bisection of Yin and Yang
- Bisector of an imaginary angle may be real
- Bisectors and Proportions [JavaScript]
- BMO 2014, Problem 3 [JavaScript, GeoGebra]
- Bottema Shatters Japan's Seclusion [Java]
- Bottema's theorem [Java]
- An Elementary Proof of Bottema's Theorem
- Bottema's Theorem - Proof Without Words [Java, GeoGebra]
- Analytic Proof of Bottema's Theorem
- Bottema in Three Rotations
- Bottema with a Product of Rotations [JavaScript, GeoGebra]
- Bottema with Similar Triangles [JavaScript, GeoGebra]
- On Bottema's Shoulders [Java]
- On Bottema's Shoulders II [Java]
- On Bottema's Shoulders with a Ladder [JavaScript, GeoGebra]
- Yet Another Generalization of Bottema's Theorem [JavaScript, GeoGebra]
- Bottema's Point Sibling

- Bottles in a Wine Rack [Java]
- Bounded Distance
- Bounds for the Sum of Distances to the Vertices [JavaScript]
- Brahmagupta's Formula and Theorem
- Brahmagupta's Theorem [Java]
- Brahmagupta-Mahavira Identities
- Brianchon in Ellipse [Java]
- Brianchon's theorem [Java]
- Brick Wall Illusion [Java]
- Bride's Chair [Java]
- Brief introduction to Rational Trigonometry
- Brocard Point and a Relation of Circumradii
- Broken Chord Theorem [Java]
- Broken Line in Triangle
- Building a Bridge [Java]
- Building Bridges [Java]
- Bulging lines illusion [Java]
- Butterfly Theorem
- A Better Butterfly Theorem
- Butterflies in Quadrilaterals and Elsewhere
- Butterfly in Ellipse [Java]
- Butterflies in Hyperbola
- The Plain Butterfly Theorem [Java]
- Butterfly theorem, a Projective Proof
- Butterflies in Similar Co-axial Conics
- Butterfly Trigonometry
- Butterfly in Kite
- Butterfly with Menelaus
- Butterfly in Parabola
- Areal Butterflies
- Butterflies in a Pencil of Conics [JavaScript, GeoGebra]
- Butterfly in Inscriptible Quadrilateral
- Butterfly via Ceva
- Butterfly via the Scale Factor of the Wings
- Butterfly by Midline
- General Butterfly in Pictures
- Piecewise Carpets in Parallelogram
- Pinning Butterfly on Radical Axes [Java]
- The Lepidoptera of the Circles [Java]
- The Lepidoptera of the Quadrilateral
- The Lepidoptera of the Triangle
- Two Butterflies Theorem [Java]
- Two Butterflies Theorem II [Java]
- Two Butterflies Theorem III [Java]
- Two Butterflies Theorem as a Porism of Cyclic Quadrilaterals [JavaScript, GeoGebra]
- Two Butterfly Theorems by Sidney Kung

- Cabart's Collinearity
- Camouflaged Butterfly
- Cantor Set and Function
- Cantor's Theorem [Java]
- Carnot's Theorem
- Carnot's Theorem
- Carnot's Theorem from Ptolemy's Theorem
- Carnot's Theorem (Generalization of Wallace's theorem) [Java]
- Carnot's Theorem for Conics
- Carpet With a Hole [Java]
- Carpets Theorem [Java]
- Carpets in a Parallelogram [Java]
- Carpets in a Quadrilateral [Java]
- Carpets in a Quadrilateral II [Java]
- Carpets in Right Triangle
- Carpets Theorem With Parallelograms [Java]
- Two Rectangles in a Rectangle [Java]
- Carpets in Hexagon
- Round Carpets
- Carpets in Triangle [JavaScript, GeoGebra]
- Carpets in Triangle, II [JavaScript]

- Casey's Theorem [Java]
- Three Points Casey's Theorem [Java]

- Cassini's Ovals and Geometric Optimization [JavaScript, GeoGebra]
- centers of similitude
- Centroid, a Characteristic Property Of
- Centroid and Circumcenter in Isosceles Tetrahedra
- Centroid and Incenter in Isosceles Tetrahedra
- Centroid on the Incircle in Isosceles Triangle
- Centroid on the Incircle in Right Triangle
- Centroids and Circumcenters
- Centroids in a Polygon [Java]
- Cevian Parallelogram [JavScript, GeoGebra]
- Chasing Angles Among Angle Bisectors [JavaScript]
- Chasing Angles in Pascal's Hexagon [Java]
- Circle, Isosceles Triangle and Fixed Point [Java]
- Circle Center by Paperfolding
- Circle Centers on Radical Axes [Java]
- Circle Chains on Napoleon Triangles [Java]
- Circle Concurrence on Circumcircle/a> [JavaScript, GeoGebra]
- Circle in a Square Inscribed in a Circle [Java]
- Circle Rotations and Fixed Points
- Circles in Barycentric Coordinates
- Circles on the sides of a triangle from the 2005 Austrian MO
- Circles Tangent to Circumcircle [Java]
- Circles Tangent to Medians at the Centroid [JavaScript, GeoGebra]
- Circles with Tangent Diameters [Java]
- Ceva and Menelaus Meet on the Roads
- Ceva in Circumscribed Quadrilateral
- Ceva's Theorem
- Ceva's Theorem and Fibonacci Bamboozlement [Java]
- A Faulty Dissection [Java]

- Cevian Cradle [Java]
- Cevian Cradle II [JavaScript, GeoGebra]
- Cevian Nest [Java]
- Cevian Triangle [Java]
- Cevians And Semicircles [JavaScript]
- Cevians Through the Circumcenter
- Chain of Inscribed Circles [Java]
- Chaos, Emergence of [Java]
- Characteristic Property Of Right Triangles
- Chasles' Theorem
- Cherchez le quadrilatère cyclique [Java]
- Cherchez le quadrilatère cyclique II [Java]
- Chords, Concurrency and Orthic Triangle [Java]
- Chromatic Number of the Plane
- Chvatal's Art Gallery Theorem [Java]
- Circle and Hyperbola as Lighthouse Curves
- Circle and Hyperbola as Lighthouse Curves II
- Circle Crosses Triangle [Java]
- Circle Concurrency and Spiral Similarity [Java]
- Circle Division by Euclid and Leonardo [Java]
- Circle of Apollonius in Equilateral Triangle
- Circle of Similitude [Java]
- Circle Rotations and Fixed Points [JavaScript, GeoGebra]
- Circle through the Circumcenter [Java]
- Circle through the Incenter [Java]
- Circle through the Incenter And Antiparallels [Java]
- Circle-Stacking Theorem [Java]
- Circles And Parallels [Java]
- Circles and Semicircles in Rectangle [Java]
- Circles Cover a Quadrilateral [Java]
- Circles in a Circular Segment
- Circles in a Regular Polygon [Java]
- Circles in Morley's Triangles [Java]
- Circles Lined on the Legs of a Right Triangle [Java]
- Circles On Cevians [Java]
- Circles through the Orthocenter [Java]
- Circles with Equal Collinear Chords [Java]
- Circular Poggendorff Illusion [Java]
- Circle Inscribed in a Circular Segment [Java]
- Circumcenter and Orthocenter
- Circumcenter and Orthocenter Are Isogonal Conjugate
- Circumcenter on Angle Bisector [Java]
- Circumcevian Triangle [Java]
- Classification of Quadrilaterals [Java]
- Cleavance Center [Java]
- Cleaver [Java]
- Clifford Algebras
- Clifford's Chain [Java]
- Climbing Pyramidal Slopes
- Clough's theorem: the simplest proof [JavaScript, GeoGebra]
- Coaxal Circles on Perpendicular Bisector [Java]
- Coaxal Circles Theorem [Java]
- Collage Theorem [Java]
- Collinear Intersections and Products of Ratios [JavaScript, GeoGebra]
- Collinearity from the IMO 2013 (Problem 4) [Javacript, GeoGebra]
- Collinearity in Bicentric Quadrilaterals [Java]
- Collinearity in Tangent Circles
- Collinearity via Concyclicity [Java]
- Collinearity with the Orthocenter [Java]
- Color Cycling on the Mandelbrot Set [Java]
- Coloring Plane with Three Colors
- Coloring Points in the Plane
- Common Centroids Lead to Equilateral Triangle [JavaScript, GeoGebra]
- Common Chord and a Tangent [Java]
- Common Tangents to Two Circles I [Java]
- Common Tangents to Two Circles II [Java]
- Compass Only Construction - A Chord Tangent to an Inner circle [Java, GeoGebra]
- Complete Quadrilateral [Java]
- Complex Numbers and Geometry
- >Concurrence in Right Triangle
- Concurrence on a Circle [JavaScript, GeoGebra]
- Concurrence Not from School Geometry [Java, GeoGebra]
- Concurrency of Medians and Medial Triangles
- Concurrency of the Altitudes in a Triangle - Trigonometric Proof
- Concyclic Points at the IMO 2014 [JavaScript, GeoGebra[
- Concyclicity in Rectangle [Java]
- Concurrence in Equilateral Triangle [JavaScript,GeoGebra]
- Concurrence of Ten Nine-Point Circles [JavScript, GeoGebra]
- Concurrency in the Intouch Triangle [Java]
- Concurrent and Parallel Lines in Parallelogram [JavaScript, GeoGebra]
- Concurrent Cevians and a Conic through Their Feet [JavaScript, GeoGebra]
- Concyclic Points from Midpoint of an Arc [GeoGebra, JavaScript]
- Concyclic Incenters in Bicentric Quadrilateral [JavaScript, GeoGebra]
- Concyclic Points in Inscriptible Quadrilateral [JavaScript, GeoGebra]
- Concyclicity from Collinearity [JavaScript,GeoGebra]
- Concyclicity in Two Semicircles [JavaScript, GeoGebra]
- Concyclic Points of Two Ellipses with Orthogonal Axes [JavaScript, GeoGebra]
- Condition to Have a 60 Degrees Angle
- Concyclic Circumcenters: A Dynamic View [Java]
- Concyclic Points in a Triangle
- Concyclic Points in Bride's Chair [Java]
- Concyclic Points in Equilateral Bumps [Java]
- Conic from Parallel Chords [JavaScript, GeoGebra]
- Conic in Hexagon [Javascript, GeoGebra]
- Conic in Mixtilinear Incircles [JavaScript, GeoGebra]
- Conic Sections
- Conic Sections as Loci of Points [Java]
- Conics Intersecting Sides Of A Triangle [JavaScript, GeoGebra]
- Conics in Triangle [JavaScript, GeoGebra]
- Conics Related To In- and Excircles [JavaScript, GeoGebra]
- Conjugate Diameters in Ellipse [Java]
- Consecutive Isosceles Decomposition [Java]
- Constant Chord
- Constrained Area in Triangle
- Constant Ratio on Circle [JavaScript, GeoGebra]
- Construct Triangle from Angle, Inradius, and Altitude [JavaScript, GeoGebra]
- Construct Triangle by Angle, Median, and Circumradius [JavaScript, GeoGebra]
- Construct Triangle by Angle Bisector, Altitude, and Side [JavaScript, GeoGebra]
- Construct Triangle by Angle, Altitude and Median [JavaScript, GeoGebra]
- Construct Triangle from Altitude, Median and Inradius [JavaScript, GeoGebra]
- Constructing a triangle from its angle bisectors is in general impossible
- Construction: Parallel Line through Point
- Construction and Properties of Mixtilinear Incircles [JavaScript, GeoGebra]
- Construction and Properties of Mixtilinear Incircles 2 [JavaScript, GeoGebra]
- Construction of a Cyclic Quadrilateral
- Construction of a Square from the 2008 Austrian MO
- Construction of a Triangle from an Angle, Circumcenter and Incenter
- Construction of a Triangle from the Circumcenter, Orthocenter and Incenter
- Construction of a Triangle from the Circumradius, Inradius, and an Altitude
- Construction of a Triangle from a Side, the Median and the Angle Bisector
- Construction of a Triangle from Two Vertices and the Centroid
- Construction of an Oval - the Roman Way [Java, GeoGebra]
- Construction of Conics from Pascal's Theorem [Java]
- Construction of Regular Pentagon by H. W. Richmond
- Construction of Thebault Circles [JavaScript, GeoGebra]
- Construction of the Angle Bisector [Java]
- Construction of the Perpendicular Bisector [Java]
- Construction of Triangle from Side, Angle, and that Angle's Bisector
- Construction problem [Java]
- Constructions Related To An Inaccessible Point
- Construction with the Compass Only
- Continuous Line Illusion [Java]
- Convex Polygon Is the Intersection of Half Planes [Java]
- Copernicus' Theorem [Java]
- Proof of Copernicus' Theorem [Java]

- Construction with Optimization in Angle - Problem the 1979 USA Mathematical Olympiad
- cos(36°) = (1 +√5)/4
- cos 75 + cos 45 = cos 15
- Cosine Law
- Laws of Sines and Cosines [Java]
- The Illustrated Law of Cosines
- The Law of Cosines: a proof without words [Java]
- The Law of Cosines for 60° and 120°
- The Law of Cosines: An Unfolded Variant [Java]
- The Law of Cosines (Independent of the Pythagorean Theorem)
- The Cosine Law by Similarity
- The Law of Cosines - Another PWW [Java, GeoGebra]
- The Law of Cosines - Yet Another PWW
- Law of Cosines by Ancient Sliding [JavaScript, GeoGebra]
- The Cosine Law: PWW by S. Kung
- The Law of Cosines and the Law of Sines Are Equivalent

- Counting Triangles and Segments in a Polygon [Java]
- Cross Points in a Polygon [Java]
- Cross-Ratio
- Crossed-Lines Construction of Shapes of Constant Width [Java]
- Crossing Number of a Graph
- Cube Counting Ambiguity [Java]
- Cultivating Regular Pentagons
- Curious Irrationality in Square
- Curry's Paradox [Java]
- Cut the Cone [Java]
- Cut the Cube [Java]
- Cutting a Hole in Half [JavaScript, GeoGebra]
- Cut the Cylinder [Java]
- Cutting Circle to Rearrange Two Dots [JavaScript]
- Cutting Squares
- Cutting Triangle in Two by a Line through a Point [Java, GeoGebra]
- Cutting Triangles off Regular Hexagon
- Cyclic Hexagon [Java]
- Cyclic Quadrilateral, Angle Bisector And Isosceles Triangle
- Cyclic Quadrilateral, Concurrent Circles and Collinear Points [Java]
- Cyclic Quadrilateral from the USAMO
- Cycloids [Java]
- Dan Sitaru's Inequality with Tangents II
- Dancing Rectangles Model Auxetic Behavior [Java]
- Dancing Squares or a Hinged Plane Tessellation [Java]
- Dao's Archimedean Twins [JavaScript, GeoGebra]
- Dao's Archimedean Twins - Second Pair [JavaScript]
- Dao's Archimedean Twins - Third Pair [JavaScript]
- Dao Thanh Oai's Invariant
- Dao's Variant of Thébault's First Problem [JavaScript, GeoGebra]
- David Richeson's Extention of an Old Japanses Theorem [Java]
- Day's Sine Illusion [Java]
- Decompose Cyclic Quadrilaterals into k≥4 Cyclic Quadrilaterals
- A Decomposition of Isosceles Triangles into 4 Isosecles Triangles
- Delboeuf Illusion [Java]
- Delian Problem Solved [Java]
- Desargues' Hexagon [Java, GeoGebra]
- Desargues in the Bride's Chair (with Pythagoras)
- Desargues' Theorem [Java]
- Determination ofπ
- Diagonal Count [Java]
- Diagonals in a Cyclic Quadrilateralli>Diagonals in a Polygon Parallel to Sides <
- Diameters and Chords [Java]
- Dimensionless Inequality in the Euclidean Plane
- Directly Similar Figures [Java]
- Disappearing Lines puzzle [Java]
- Discovery of Duane DeTemple [Java]
- Dissection of a 10×13 Rectangle into Two Chessboards
- Dissection of a Vase [Java]
- Dissection of Cyclic Quadrilateral [Java]
- Dissection of Triangle into Rhombus [Java]
- Dissection of Triangle into Rhombus by Hubert Shutrick [Java]
- Distance
- Distance Between Projections
- Distance between the Orthocenter and Circumcenter
- Distance Formula
- Distorted Lines Illusion [Java]
- Divergent Spirals Illusion [Java]
- Divide a Circle into N Parts of Equal Area
- Divide a segment into n equal parts
- Dividing a Segment by Paper Folding
- Dividing a Segment into N parts: Besteman's Construction [Java]
- Dividing a Segment into N parts: Besteman's Construction II [Java]
- Dividing a Segment into N parts: GLaD Construction [Java]
- Dividing a Segment into N parts: SaRD Construction [Java]
- Al-Nayrizi's Construction [Java]
- Euclid's Segment Division [Java]
- Similar Right Triangles [Java]

- Divide Triangle by Lines Parallel to Base [JavaScript, GeoGebra]
- Dividing Evenly a Quadrilateral [Java]
- Dividing Evenly a Quadrilateral II [Java]
- Dorin Marghidanu's Inequality with Maximum Side
- Double Generation Theorem [Java]
- Drawing circles [Java]
- Droz-Farny Circles [Java]
- Droz-Farny Line Theorem [Java]
- Droz-Farny Theorem - an Analytic Solution [JavaScript, GeoGebra]
- Dual of Maxwell's Theorem
- Duplication of the Cube
- Dynamic Construction of Ellipse and Other Curves [Java]
- Dynamic Software as Serendipity Enhancement [Java, GeoGebra]
- A. G. Samosvat's Proof by Dissection of the Pythagorean Theorem (#104) [GeoGebra]
- E. W. Dijkstra's Proof of the Pythagorean Theorem [Java]
- Early Refinement of the Ionescu-Weitzenbock Inequality
- Easy Construction of Bicentric Quadrilateral [Java]
- Easy Construction of Bicentric Quadrilateral II [Java]
- Egyptian Triangle By Paper Folding
- Egyptian Triangle By Paper Folding II
- Egyptian Triangle By Paper Folding III
- Eight Equal Tangents [Java]
- Eight Point Circle [Java]
- Elementary Introduction into the Concept of Area
- Ellipse Between Two Circles [Java]
- Ellipse in Arbelos [Java]
- Ellipse Touching Sides of Triangle at Midpoints [Java, GeoGebra]
- Emil Stoyanov's From Reflections to Altitudes
- Emil Stoyanov's New Year's Problem
- Emil Stoyanov's New Year's Problem, a Sequel
- Equal And Perpendicular Segments in a Square
- Equal Angles in Two Circles [Java]
- Equal Angles in Two Circles II [Java]
- Equal areas In Circle [JavaScript]
- Equal Areas in Equilateral Triangle [Java]
- Equal Areas In Parallelogram à la Pythagoras [Java]
- Equal Areas in Regular 2n-gons [Java]
- Equal Chords in Crossing Circles [Java]
- Equal Circles, Medial Triangle and Orthocenter [Java]
- Equal Incircles Theorem [Java]
- Equiangular p-gons
- Equichordal points: Just Do It [Java]
- Equidecomposition of a Rectangle and a Square [Java]
- Equidecomposition of Two Rectangles [Java]
- Equidecomposition of a Triangle and a Rectangle [Java]
- Equidecomposition of a Triangle and a Rectangle II [Java]
- Equidecomposition of Two Parallelograms [Java]
- Equilateral and 3-4-5 Triangles [Java]
- Equilateral triangle and squares
- Equilateral Triangle from Equilateral Triangle
- Equilateral Triangle in Equilateral Triangle [JavaScript, GeoGebra]
- Equilateral Triangle on a Closed Curve [JavaScript, GeoGebra]
- Equilateral Triangle on Angle Bisectors
- Equilateral Triangle on Parallel Lines [Java]
- Equilateral Triangle on Parallel Lines II
- Equilateral Triangle on Three Lines [JavaScript, GeoGebra]
- Equilateral Triangle in Square and Its Circumcircle
- Equilateral Triangle in Square with the Cevians through Its Apex
- Equilateral Triangle in Square And the Pedal Circle of Its Apex
- Equilateral Triangle, Straight Line and Tangent Circles [Java]
- Equilateral Triangles and Incircles in a Square
- Equilateral Triangles formed by Circumcenters [JavaScript, GeoGebra]
- Equilateral Triangles on Diagonals of Antiequilic Quadrilateral [Java]
- Equilateral Triangles On Sides of a Parallelogram [Java]
- Equilateral Triangles On Sides of a Parallelogram II [Java]
- Equilateral Triangles on Sides of a Parallelogram III [JavaScript, GeoGebra]
- Equilateral Triangles on Sides of a Quadrilateral [Java]
- Equilic Quadrilateral I, a Flawed Proof [Java]
- Equilic Quadrilateral I, A Variation [Java]
- Equilic Quadrilateral II [Java]
- Erdös-Mordell Inequality
- Escher's Theorem [Java]
- Euclid's Fifth Postulate
- Euclid's
*Elements*Reference Page - Euclid I.43 [Java]
- Euclid I.43 Extended [Java]
- Euclidean Construction of Center of Ellipse [Java]
- Euclidean Construction of Tangent to Ellipse
- Euler Inequality in Triangle
- Euler Line Cuts Off Equilateral Triangle [Java]
- Euler Line and 9-Point Circle [Java]
- Euler Line Through a Vertex
- Euler's Formula and Poncelet Porism
- Euler Line in a Triangle with a 60 Degrees Angle
- Every Parallelogram Is a Rectangle
- Excircle in Equilateral Triangle
- Excircles in Trapezoid
- Exeter Point [Java, GeoGebra]
- Existence of the Circumcenter [Java]
- Existence of the Orthocenter [GeoGebra]
- Existence of the Euler Line: An Elementary Proof [Java]
- Existence of the Incenter: a Second Look
- Experimentation with Dynamic Geometry Software: An Example [Java]
- Exploring Vecten's Wreaths with Linear Algebra
- Expressions Invariant under Projecive Mappings
- Exterior Angle Theorem - an appreciation
- External Angle Bisector [Java]
- Extouch Triangle in Poncelet Porism [Java]
- Extra Feature of Van Aubel Configuration [JavaScript,GeoGebra]
- Extras in Bottema's Configuration [JavaScritpt, GeoGebra]
- Extremal Problem in a Quadrilateral
- Extremal Distance Ratio [GeoGebra]
- Extremal Problem in a Circular Segment
- The Extreme Principle
- Eye-to-Eye Theorem I [JavaScript, GeoGebra]
- Eye-to-Eye Theorem II [JavaScript, GeoGebra]
- Eyeball Theorem [JavaScript, GeoGebra]
- Eyeball Theorem Rectified [JavaScript]
- Eyeballing a Ball [JavaScript, GeoGebra]
- Eyeballs Projected [JavaScript, GeoGebra]
- Fagnano's problem [Java]
- Faulty Symmetry
- Fermat's Hexagon [JavaScript, GeoGebra]
- Fermat in a Triangle with a 60 Degrees Angle
- Fermat point and 9-point Centers [Java]
- Fermat Point Several Times Over
- Feuerbach's Theorem: A Proof [Java]
- Find a Common Chord of Given Length [Java]
- Find the Angle! [Java]
- Finding a Parallelogram in 3D
- Finding Circle Center By Ruler Alone [Java]
- Finding the Circumradius of the Excentral Triangle
- Five Concyclic Points [Java]
- Five Incircles in a Square [Java]
- Five Incircles Theorem [Java]
- Five Squares in Complex Numbers [Java, GeoGebra]
- Fixed Point in a Kite - Problem from the 1993 Asian Pacific MO
- Fixed Point in Isosceles and Equilateral Triangles
- Fixed Point on Perpendicular Bisector [GeoGebra, JavaScript]
- Fixed Point of Circles Orthogonal to the Given One [Java]
- Fixed points from 2007 Irish Mathematical Olympiad
- Fleury's Algorithm and Euler's Paths and Cycles [Java]
- FJG Capitan's Sangaku
- Focal Definition of Ellipse [Java]
- Focal Definition of Parabola [Java, GeoGebra]
- Focus and Directrix of Ellipse [Java]
- Focus on the Eyeball Theorem [JavaScript, GeoGebra]
- Folding Square in a Line through the Center [Java, GeoGebra]
- Fold Square into Equilateral Triangle [JavaScript]
- Following the Hilbert Curve [Java]
- Foot of Altitude and Minimum Distance [Java]
- For Equality Choose Angle Bisector [JavaScript, GeoGebra]
- For every object there is a distance at which it looks its best.
- Ford's touching circles
- Four Centroids and Parallels [Java]
- Four Circles and a Line [GeoGebra]
- Four Circles In a Triangle [Java]
- Four Concurrent Lines in a Cyclic Quadrilateral [Java]
- Four Construction Problems [Java]
- Four Crossing Circles [Java]
- Four Geometric Problems of Antiquity
- Four Golden Circles
- Four Hinged Squares [Java]
- Four Incident Circles [Java]
- Four Incircles in Equilateral Triangle [Java]
- Four Isosceles Triangles Hinged at Vertices [JavaScript, GeoGebra]
- Four 9-Point Circles in a Quadrilateral [Java]
- Four Pedal Circles [Java]
- Four Touching Circles [Java]
- Four Touching Circles II [Java]
- Four Touching Circles III [Java]
- The Four Touching Circles Problem IV [Java, GeoGebra]
- Four Triangles, One Circle [Java]
- Four Turtles (or Bugs, or Dogs, etc.) [Java]
- Fractal curves and dimension [Java]
- François Viète's Reduction of CCC to PCC [Java, GeoGebra]
- Friendly Kiepert's Perspectors [Java]
- From 3 to Golden Ratio in Semicircle
- From Angle Bisector to 120°120 degrees Angle
- From Arbitrary Hexagon to Regular One [JavaScript, GeoGebra]
- From Arbitrary Pentagon to Regular One [JavaScript, GeoGebra]
- From Equilateral Triangle and Square to Golden Ratio
- From Foci to a Tangent in Ellipse [Java]
- From One Collinearity to Another
- From Perpendicular Center Lines to Concyclic Points
- From Straight Line to Regular Hexagon [JavaScript, GeoGebra]
- From Triangle Inequality to Inequality in Triangle
- Fun Identity in Right Triangle
- Functions And Triangles
- Fundamental Theorem of 3-Bar Motion [Java]
- Further Arithmetic Progression in 30-60-90 Triangle
- Further Properties of Peculiar Circles
- Further properties of Van Aubel Configuration [JavaScript, GeoGebra]
- Fuss' Theorem [Java]
- Garcia's Archimedean Quadruplets [JavaScript, GeoGebra]
- Garcia's Two Circles Lemmas [JavaScript, GeoGebra]
- Garcia-Feuerbach Collinearity [JvaScript, GeoGebra]
- Garfield's Ghost Revisited - by Tony Foster
- Generalizing a Romanian Olympiad Problem [Java]
- Geometric/Trigonometric Observation/Exercise
- Geometric Illustration of a Convergent Series
- Geometric Mean In Trapezoid
- Geometric Mean Sangaku
- Geometric Meaning of the Geometric Mean
- Geometric Optimization from the Asian Pacific Mathematical Olympiad [Java]
- Geometric Proof of Hlawka's Inequality
- Geometric Proofs Of the Irrationality of Square Roots
- Geometry, Algebra, and Illustrations
- Gergonne and Medial Triangles Are Orthologic [Java]
- Gergonne and Soddy Lines Are Perpendicular [Java]
- Gergonne in Ellipse [Java]
- Gergonne and Van Obel Theorems
- Getting the first digits of Pi by counting collisions
- Gion Shrine Problem
- Given Parabola, Find Axis
- Glide Reflection [Java]
- Golden Ratio in Geometry
- Golden Ratio and Midpoints
- Golden Ratio in an Irregular Pentagon
- Golden Ratio in an Irregular Pentagon, Construction I [Java]
- Golden Ratio in an Irregular Pentagon, Construction II [Java]
- Golden Ratio in Isosceles Triangle
- Golden Ratio in Isosceles Triangle II
- Golden Ratio in Equilateral Triangle on the Shoulders of George Odom
- Golden Section in Two Equilateral Triangles
- Golden Section in Two Equilateral Triangles, II
- Golden Ratio via Golden Rhombus
- Golden Ratio in Regular Pentagon
- Golden Ratio in Circle - in Droves
- Golden Ratio via van Obel's Theorem
- Golden Ratio in Equilateral Triangles
- Golden Ratio in Square
- Golden Ratio in Hexagon
- Golden Ratio in Two Squares
- Golden Ratio in Two Equilateral Triangles
- Golden Ratio As a Mathematical Morsel
- Golden Ratio in Inscribed Equilateral Triangles
- Golden Ratio in a Rhombus
- Golden Ratio in Five Steps
- Golden Ratio in Mixtilinear Circles
- Golden Ratio in Isosceles Right Triangle, Square, and Semicircle
- Golden Ratio With Two Equal Circles And a Line
- Golden Ratio in a Chain of Polygons, So to Speak
- Golden Ratio With Two Unequal Circles And a Line
- Golden Ratio In a 3x3 Square
- Golden Ratio In a 3x3 Square II
- Golden Ratio in Square
- Golden Ratio In Three Tangent Circles
- Golden Ratio In Right Isosceles Triangle
- Golden Ratio Poster
- Golden Ratio Next to Poster
- Golden Ratio In Rectangles
- Golden Ratio In a 2x2 Square: Without And Within
- Golden Ratio With Two Unequal Circles And a Line II
- Golden Ratio in Equilateral and Right Isosceles Triangles
- Golden Ratio in a Butterfly Astride an Equilateral Triangle
- Another Golden Ratio in Regular Pentagon
- Golden Ratio in 5-gon and 6-gon
- Golden Ratio in an Isosceles Trapezoid with a 60° Angle
- Golden Ratio in Circles
- Golden Ratio in Pentagon And Two Squares
- Golden Ratio in Pentagon And Three Triangles
- Golden Ratio in a Mutually Beneficial Relationship
- Star, Six Pentagons and Golden Ratio
- Golden Ratio in an Isosceles Trapezoid with a 60 degrees Angle II
- Golden Ratio in Three Regular Pentagons
- Golden Ratio in Three Regular Pentagons II
- Golden Ratio in Square And Circles
- Golden Ratio in Two Squares, Or, Perhaps in Three
- Golden Ratio in Wu Xing
- Golden Ratio In Three Circles And Common Secant
- Golden Ratio in Yin-Yang
- Golden Ratio in Pentagon: Once More
- Golden Window

- Golomb's inductive proof of a tromino theorem [Java]
- Gothic Arc [Java]
- Graph Theory [Java]
- Grebe: from Ladies' Diary to Carroll's Pillow [Java]
- Grebe's Theorem
- Greg Markowsky's Problem for Parabola [Java]
- Gregoie Nicollier's Proof of Napoleon's Theorem
- Griffiths Points in Cyclic Quadrilateral [Java]
- Griffiths' Theorem
- Half Turn, Reflection in Point [Java]
- Halving a square
- Harmonic Mean in Geometry
- Harmonic Mean Sangaku [Java]
- Harmonic Ratio
- Harmonic Ratio in Complex Domain
- Hart Circle [Java]
- Hart's Inversor [Java]
- Haruki's Lemma [Java]
- Haruki's Theorem
- Hausdorff Distance
- Hearty Munching on Cardioids [Java]
- Height/Width Interplay Illusion [Java]
- Helly's Theorem
- Hering Illusion [Java]
- Hermann Grid Illusion [Java]
- Heron's formula
- Heron's Formula: a Proof [Java]
- Heron's Problem [Java]
- Heron in Trapezoid [JavaScript, GeoGebra]
- Hexagon Parallel to Medial Triangle [Java]
- Hexagon Parallel to Orthic Triangle [Java]
- Hexagons in a Square
- Hidden Orthogonality [JavaScript, GeoGebra]
- Hinged Greek Cross Tessellation [Java]
- Hinged Squares [Java]
- Hinged Squares II [JavaScript, GeoGebra]
- Hippocrates' Squaring of a Lune [Java]
- Hippocrates' Squaring of Lunes
- Hjelmslev Theorem [Java]
- Hjelmslev's Theorem on Canvas [JavaScript]

- Hlawka in Convex Quadrilateral
- Homologous Lines under Three Spiral Similarities [Java]
- Homothety [Java]
- Homothety between In- and Excircles [Java]
- Homothety in Equilateral Triangles [JavaScript, GeoGebra]
- Homothety in Three Tangent Circles
- Homothety in Three Tangent Circles II
- Hooper's Paradox [Java]
- How Do Angle Trisectors Divide the Area?
- How Fast Does One's Shadow Grow?
- How Long Are the Angle Bisectors of a Degenerate Triangle?
- How to Construct a Radical Axis [Java, GeoGebra]
- How to Construct Tangents from a Point to a Circle [Java, GeoGebra]
- Hung Nguyen Viet's Inequality with Radicals and Chebyshev
- Hunting Right Angles [Java]
- Huygens' Problem
- Ian McGee's Observation [Java]
- IMO 1998 Problem 1
- IMO 2004, Problem 5
- IMO 2006, Problem 1
- Impossible Fork [Java]
- Impossible Frame [Java]
- Impossiblity Condition in Concurrent Cevians
- Importance of Having an Angle of 60 Degrees
- Importance of Occluders: Motion Binding [Java]
- In the Spirit of Thebault I [Java, GeoGebra]
- In the Wasan Spirit
- Incenters in Cyclic Quadrilateral [Java]
- Incidence in Feuerbach's Theorem [Java]
- Incircle in Equilateral Triangle
- Inequalities in Triangle
- An Inequality in Triangle, VII
- An Inequality in Triangle, VIII
- An Inequality in Triangle, IX
- An Inequality in Triangle, X
- An Inequality for Cevians And The Ratio of Circumradius and Inradius
- Inequality In Triangle: Sides and Angle Bisectors
- An Inequality with Sides and Medians
- An Inequality in Triangle with Sides and Medians II
- An Inequality in Triangle, with Sides and Medians III
- An Inequality in Triangle, with Sides and Sums
- An Inequality In Triangle with Sines of Half-Angles
- An Inequality in Triangle form the 1996 APMO

- Inequality in Quadrilateral
- Inequality in Rectangle
- An Inequality with a Variety of Circumradii
- Inequality with Cubes and Cube Roots
- An Inequality with Inradius and Excenters
- Inequality with Roots, Squares and the Area
- An Inequality with Two Sets of Cevians
- Infinitude of Primes - A Topological Proof
- Inradii Relation in Right Triangle
- Inscribed and Central Angles in a Circle [Java]
- Inscribed Angles [Java]
- Inscriptible and Exscriptible Quadrilaterals [Java]
- Inscriptible Quadrilateral: An Illustration [Java]
- Inscriptible Quadrilateral of Triangle Incenters [JavaScript, GeoGebra]
- Integer Chord in a Polynomial Graph
- Integer Triangles with Two Angles in the Ratio 1 : 2 [JavaScript, GeoGebra]
- Internal Tangents to Three Circles [Java]
- Interpretation of the coordinate formula for the dot product in 3D
- Intersecting Chords Theorem
- Intersecting Chords Theorem - a Visual Proof [Java, GeoGebra]
- Intersecting Chords Theorem - Hubert Shutrick's PWW [Java, GeoGebra]

- Intersections of a Circle with the Four Quadrants [Java]
- Intouch Triangle in Poncelet Porism [Java]
- Invariance in Orthodiagonal Quadrilaterals [Java]
- Invariant Area Sweep Implies Pythagorean Theorem [Java]
- Inverse Similarity through Reflections
- Inversion: Reflection in a Circle [Java]
- Inversion [Java]
- Inversion in the Incircle [Java]
- Inversion Tool
- Inversion with Negative Power [Java]
- Invert Two Circles Into Equal Ones [JavaScript, GeoGebra]

- Involution on the Projective Line
- Is Every Trapezoid Parallelogram? [Java]
- Is X a Midpoint of a Chord [JavaScript, GeoGebra]
- Isosceles Tetrahedra Characterization via Inequalities
- Isogonal Concurrencies [JavaScript, GeoGebra]
- Isogonal Lemma [JavaSCript, GeoGebra]
- Isosceles Configuration in Triangle [JavaScript, GeoGebra]
- Isosceles Tetrahedron
- Isosceles Trapezoid In Cyclic Quadrilateral [JavaScript, GeoGebra]
- Isosceles Triangle with Two Points on Base
- Isogonal and Isotomic Conjugalities [Java]
- Isogonal Concurrency [Java]
- Isogonal image of the circumcircle [Java]
- Isoperimetric Theorem and Inequality
- Isosceles on the Sides of a Triangle [Java]
- Isotomic Reciprocity [JavaScript, GeoGebra]
- Isotomy and Isogonality Hand-in-Hand [Java]
- Iterations and the Mandelbrot Set [Java]
- Iterations on a Circle Through Three Points [Java]
- Iterations on Euler Lines [Java]
- Igor Sharygin's Problem in Circumscribed Quadrilateral
- J. Casey's Additions to Euclid I.47
- Jan Stevens' proof of E. W. Dijkstra's Generalization of the Pythagorean theorem
- Joachimsthal's Notations
- John Sharp's Paradox [Java]
- Johnson Circles [Java]
- Join Circles by Given Segment [Java]
- Joined Common Chords of Napoleon's Circumcircles [JavaScript, GeoGebra]
- Jordan and Kober Inequalities, PWW
- Jordan Curve Theorem
- Joseph Keech in Bride's Chair [Java]
- Judd Illusion [Java]
- Julia sets indexing [Java]
- K. Knop's Problem with Two Regular Pentagons And an Equilateral Triangle
- Kanizsa Triangle [Java]
- Kiepert's Centroid [JavaScript, GeoGebra]
- Kiepert's Theorem [Java]
- Kiepert's Triangles Graduate to Ears of Arbitrary Shape [JavaScript, GeoGebra]
- Klamkin's Quickie via Peru Geometrico
- Knots [avi movie]
- Knots on a Torus [Java]
- Kürschak's Tile and Theorem [Java]
- La Hire's Theorem [Java]
- La Hire's Theorem [Java]
- La Hire's Theorem in Ellipse [Java]

- Langman's Paradox [Java]
- LCC: Apollonius' Problem with Two Circles and a Line [Java, GeoGebra]
- Lean Napoleon's Triangles [Java]
- Length of a Median
- Length of the diagonal of the unit square equals the square root of 2
- Lennes' Polyhedron [Java]
- Leo's Lemma, Second Application
- Leo Giugiuc's Inequality for the Medians
- Leo Giugiuc's Inequality in Triangle, Solely with Cotangents
- Leo Giugiuc's Proof of Napoleon's Theorem
- Leo Giugiuc's Trigonometric Lemma
- Leo Giugiuc's Second Lemma And Applications
- Leonardo's Petals
- Lepidoptera of the Circles [Java]
- Leuenberger's Inequality for Medians, Inradius and Circumradius
- Lighthouse at Fermat Points [JavaScript, GeoGebra]
- Line IO in Bicentric Quadrilaterals
- Line Not Through a Center of Similarity [JavaScript, GeoGebra]
- Line Through a Center of Similarity [JavaScript, GeoGebra]
- Line through a Point in an Angle
- Line, Circle, and Fixed Points [Java]
- Linear Function with Coefficients in Arithmetic Progression [Java, GeoGebra]
- Lines Crossing Circles at Vertices of Equilateral Triangle
- Lines through Circles at Vertices of Equilateral Triangle [JavaScript]
- LLC: Apollonius' Problem with Two Lines and a Circle [Java, GeoGebra]
- Lipogrammatic Proof of the Pythagorean Theorem
- Loci of points in a cube
- Locus of Points in a Given Ratio to Two Points [Java]
- Longest segment
- Longitude, Latitude and Distance to the Equator
- Looking Back at Bottema [JavaScript, GeoGebra]
- Luca Moroni's Problem In Equilateral Triangle
- Mach's Conservation of Area and the Pythagorean Theorem
- MacLaurin's Construction of Conics [Java]
- Maimed Cake [Java]
- Malfatti's Problem [Java]
- Malfatti's Problem, Hart's Solution [Java]
- Marian Cucoanes' Inequality With Roots and Powers
- Marian Dinca's Inequality
- Mascheroni Construction of a Regular Pentagon
- Mathematical Droodles [Java]
- Mathematics in Pizzeria [Java]
- MathPro Logo [Java]
- Maximal Properties of the Pythagorean Relation
- Maximum Area Property of Equilateral Triangles
- Maximum Area Property of the Medial Triangle
- Maximum Perimeter Property of the Incircle [Java]
- Maximum Ratio of Similarity - Belarus Olympiad Problem
- Maxwell's Theorem [Java]
- May the Product of Planes Be a Sphere?
- McDougall's Generalization of Ptolemy's Theorem
- Mechanical Proofs of the Pythagorean Theorem
- Median in Touching Circles [Java]
- Medians
- A Median Surprise [JavaScript, GeoGebra]

- Medians in a Quadrilateral [Java]
- Medians in a Triangle Meet at the Center: a Second Look
- Meisters' Two Ears Theorem
- Menelaus Theorem [Java]
- Metric Relations in a Triangle
- Mickey Might Be a Red Herring in the Mickey Mouse Theorem
- Midline in Quadrilateral [Java, GeoGebra]
- Midline in Similar Triangles [Java]
- Midline in Trapezoid [Java, GeoGebra]
- Midline in Triangle [Java, GeoGebra]
- Midpoint Reciprocity in Napoleon's Configuration [JavaScript,GeoGebra]
- Midpoints and Orthogonality in Isosceles Triangles [Java]
- Midpoints from Gergonne Triangle [Java]
- Midpoints of the Lines Joining In- and Excenters [Java]
- Miguel's Area of Square [JavaScript, GeoGebra]
- Miguel's Tangents: Modern Day Sangaku [JavaScript, GeoGebra]
- Miguel Ochoa's Chords And Tangents [JavScript, GeoGebra]
- Miguel Ochoa's van Schooten Is a Slanted Viviani [JavScript, GeoGebra]
- Miguel Ochoa's van Schooten Like Theorem [JavaScript, GeoGebra]
- Miguel Ochoa's van Schooten Like Theorem II [JavaScript, GeoGebra]
- Miguel Ochoa's van Schooten Like Theorem III [JavaScript, GeoGebra]
- Miguel's Special Trapezoid
- Mikhalev's Octahedrons
- Minesweeper Theorem
- Miquel's Point [Java]
- Miquel's Point of a 4-line Via Spiral Similarity [Java]
- Miquel's Theorem for Circles [Java]
- Miquel Circumcenters [JavaScrirpt, GeoGebra]
- Mirror on the Wall [Java]
- Mirror property of the altitudes [Java]
- Mirror Property of Altitudes via Pascal's Hexagram [Java]
- Mixing Incenter And Orthocenter in Greece
- Mixtilinear Circles and Concurrence [Java]
- Modern Day Sangaku
- Moebius Strip [avi movie]
- Möbius' Strip [Java]
- Models and Metamathematics
- Moment of Inertia of a Regular Polygon [JavaScript]
- Moments in a Peculiar Cyclic Polygon
- Monge via Desargues [Java]
- Monge via Desargues II [Java]
- More of More of Gloden Ratio in Equilateral Triangles
- Morley Constellation [Java]
- Morley's Miracle [Java]
- Doodling and Miracles [Java]
- Morley's Pursuit of Incidence [Java]
- Lines, Circles and Beyond [Java]
- Morley's Theorem, G. Zsolt Kiss' proof [Java]
- Morley's Theorem, R. Smyth's Proof
- Proof by H. D. Grossman
- Proof by R. J. Webster
- On Motivation and Understanding [Java]
- Bankoff's Conundrum
- B. Bollobás' proof
- B. Bollobás' Trigonometric Proof of Morley's Theorem
- L. Giugiuc's Proof of Morley's Theorem
- Morley's Redux and More [Java]
- An Unexpected Variant
- Morley's Theorem: Proof by B. Stonebridge and B. Millar
- Morley's Theorem: Proof by H. Shutrick
- Morley's Theorem: Taylor and Marr's Proof [JavaScript, GeoGebra]
- Original Taylor and Marr's Proof [JavaScript, GeoGebra]
- Morley's Theorem: Second Proof by Roger Smyth
- Morley's Theorem: A Proof That Needs Fixing
- A Vector-based Proof of Morley's Trisector Theorem
- Dijkstra's Proof of Morley's Theorem
- Backward Proof of Morley's Theorem by B. Stonebridge
- Morley's Equilaterals, Spiridon A. Kuruklis' proof [JavaScript, GeoGebra]
- Proof by A. Robson
- J. Arioni's Proof of Morley's Theorem

- Morphing [Java]
- Müller-Lyer Illusion [Java]
- Multifaceted Cork [Java]
- Multiplication of Points on a Circle [JavaScript,GeoGebra]
- Multiplication of Points on an Ellipse [JavaScript, GeoGebra]
- Munching on Circles
- Munching on Inscribed Angles
- More On Inscribed Angles [Java]

- My logo
- Nagel Line [Java]
- Nagel point [Java]
- Nagel Point and Centroid on Adjacent Isosceles Triangles
- Nagel Point of the Medial Triangle [Java]
- Nagel Point on the Incircle in Isosceles Triangle
- Nagel's Theorem [Java]
- Napoleon's Hexagon [JavaScript, GeoGebra]
- Napoleon's Theorem
- Napoleon-Barlotti Theorem [Java]
- Napoleon on Hinges [Java]
- Napoleon on Hinges in GeoGebra [JavaScript, GeoGebra]
- Napoleon's Relatives [Java]
- Napoleon's Theorem, a generalization
- Napoleon's Theorem by Plane Tesselation [Java]
- Napoleon's Theorem by Transformation [Java]
- Generalization of Napoleon's Theorem [Java]
- Napoleon's Propeller [Java]
- Napoleon's Theorem via Two Rotations [Java]
- Napoleon's Theorem: A third proof with complex numbers [Java]
- Napoleon's Theorem by Vectors and Trigonometry [Java, GeoGebra]
- Yet Another Analytic Proof of Napoleon's Theorem

- Necker Cube [Java]
- Neuberg Cubic [Java, GeoGebra]
- Neuberg Sangaku [Java]
- Newly Born Pair of Siblings to Archimedes' Twins [Java]
- Newton's Construction of Conics [Java]
- Newton's Theorem [Java]
- Nine Point Center in Square
- Nine Point Circle [Java]
- Nine Point Circle: an Elementary Proof [Java]
- No Equilateral Triangles, Please [Java]
- Nobbs' Points, Gergonne Line [Java]
- Non-Eclidean Geometries
- No-Pedal Collinearity [Java]
- Not So Hidden Homotheties [JavaScript, GeoGebra]
- Novel Concurrency of Perpendicular Bisectors [JavaScript, GeoGebra]
- Number of Regions N Lines Divide Plane
- Occluded Wheel Illusion [Java]
- Olof Hanner's Jigsaw Puzzle [Java]
- On the Difference of Areas
- One More Property of Equilateral Triangles
- One More Seven Circles Theorem [JavaScript, GeoGebra]
- One Sheet Hyperboloid [Java]
- A One-Sided Inequality in Triangle
- One Triangle from Another
- One Triangle from Another II
- Optimal Quadrilateral Inscribed in a Square
- Optimal Quadrilateral Inscribed in Square, PWW [JavaScript, GeoGebra]

- Optimization in a Crooked Trapezoid
- Optimization in Parallelepiped
- Optimization Problem in Acute Angle [Java]
- Octagon in Parallelogram: Overlapping Regions [Java]
- Octagon in Parallelogram [Java]
- Optical Property of Ellipse [Java]
- Orbison illusion [Java]
- Orthic Semiperimeter [Java, GeoGebra]
- Orthic Triangle in a Triangle with a 120 degrees angle
- Orthogonal Lines, Midpoints, and Collinearity [Java, GeoGebra]
- Orthogonality in Isogonal Conjugacy [JavaScript, GeoGebra]
- Orthocenter and Three Equal Circles [Java]
- Orthocenters
- Orthocenters of Two Triangles Sharing Circumcenter and Base [Java]
- Orthocentric System From Rectangle [Java]
- Orthodiagonal and Cyclic Quadrilaterals [Java]
- Orthogonality in Isosceles Triangles [Java]
- Orthogonality in Two Squares [JavaScript, GeoGebra]
- Orthologic Triangles in a Quadrilateral [Java]
- Orthopole [Java]
- Out of Pentagon Sangaku
- Packing shapes in a plane
- Padoa's Inequality
- Pairs of Areas in Equilateral Triangle
- Pairs of Homologous Lines under Spiral Similarities [Java]
- Pairs of Incircles in a Quadrilateral [Java]
- Pantograph [Java]
- Paper Folding & Cutting Sangaku
- Paper Folding Geometry
- Paper strip activities [avi movies]
- Paper strip activities, two strips
- Pappus' Generalization of Euclid I.47 [Java]
- Pappus' Theorem [Java]
- Dual to Pappus'Theorem [Java]

- Parabola [Java]
- Parabola and Abutting Equilateral Triangles
- Parabolas Related to the Orthic Triangle [JavaScript, GeoGebra]
- Parabolic Mirror, Illustration [Java]
- Parabolic Mirror, Theory [Java]
- Parabolic Reciprocity [JavaScript, GeoGebra]
- Parabolic Sieve of Prime Numbers
- Paragon [Java]
- Parahexagon [Java]
- Parallel Chords [Java]
- Parallel Chords II [Java]
- Parallel Chords in Conics [Java, GeoGebra]
- Parallel Chords in Ellipse [Java]
- Parallel Chords in Crossing Circles [Java]
- Parallel Lines in a Cyclic Quadrilateral [Java]
- Parallel Lines in a Quadrilateral II [Java] Parallel Lines in a Quadrilateral
- Parallel Lines in Rhombus
- Parallel Lines in a Triangle [Java, GeoGebra]
- Parallels through the Vertices of Equilateral Triangle
- Parallelogram and Ellipses [Java, GeoGebra]
- Parallelogram and Four Equilateral Triangles [JavaScript, GeoGebra]
- Parallelogram and Similar Triangles [Java]
- Parallelogram Illusion [Java]
- Parallelogram in Four Circles [JavaScript, GeoGebra]
- Parallelogram in Parallelogram And in Projection [JavaScript, GeoGebra]
- Parallelogram in Trapezoid
- Parallelogram Iterations [Java]
- Parallelogram Law [Java]
- Parallelogram Law: A PWW [Java]
- Parallelogram Law: A Tessellation [Java]
- Parallelogram with Side Lines through Fixed Points [JavaScript, GeoGebra]
- Partition of point sets in a plane
- Partitioning 3-Space with Circles
- Partitioning a Circle
- Pascal: Necessary and Sufficient [Java]
- Pascal in a Cyclic Quadrilateral [Java]
- Pascal Lines: Steiner and Kirkman Theorems [Java]
- Pascal Lines: Steiner and Kirkman Theorems II [Java]
- Pascal's theorem [Java]
- Peacock's Tail Sangaku
- Peaucellier Linkage [Java]
- Pedal Collinearities [Java]
- Pedal Parallelogram [JavScript, GeoGebra]
- Pedal Polygons [Java]
- Pedal Property in Equilateral Triangle
- Pedal SimilarityPedal Triangle and Isogonal Conjugacy [Java]
- Pedal Triangles of Inverse Points [JavaScript, GeoGebra]
- Pedoe's Theorem [Java]
- Pencils of Cubics
- Pentagon, construction of
- Pentagon And Decagon, Both Regular
- Pentagon in a Semicircle [Java]
- Pentagon Proportions Sangaku
- Perimeters of Convex Polygons, One within the Other
- Perimeters of Parallelogram And Rhombus [JavaScript, GeoGebra]
- Periodic patterns in sin(N) [Java]
- Perpendicular Bisectors in an Inscriptible Quadrilateral [Java]
- Perpendicular Bisectors in an Inscriptible Quadrilateral II [Java]
- Perpendicular lines in a cyclic quadrilateral from 1975 Canadian Mathematical Olympiad
- Perpendiculars in Parallelogram [JavaScript, GeoGebra]
- Perspective Triangles in Circle
- Pick's Theorem [Java]
- Phantom Circle and Recaptured Symmetry
- Planar Sets with Integer Distances between Points
- Plane Filling Curves [Java]
- Plane Isometries
- Plane Isometries As Complex Functions
- Plato's Geometric Numbers: can you better Sam Loyd?
- Pleasant Proportions in Triangle
- Poggendorff's Illusion
- Point common to two similar rectangles [Java]
- Point in a Square
- Point on Bisector in Right Angle
- Points Generated by the Nine Points
- Points on Incircle: Another Look
- Polar Circle [Java]
- Poles and Polars [Java]
- Poles, Polars and Orthogonal Circles [Java, GeoGebra]
- Poles, Polars and Quadrilaterals [Java]
- Pole and Polar with respect to a Triangle [Java]

- Polygon in a Rectangle
- Polygons: formality and intuition [Java]
- Polygons Formed by Perpendicular Bisectors [Java]
- Pompeiu's Theorem
- Poncelet's Porism [Java]
- Poncelet's Porism in Ellipses [Java]
- Poncelet's Theorem [Java]
- Ponzo Illusion [Java]
- Ponzo Illusion II [Java]
- Possible or Impossible? [Java]
- Power of a point with respect to a circle
- PCC: Apollonius' Problem with Two Circles and a Point [Java, GeoGebra]
- PLC: Apollonius Problem with a point, a line, and a circle [Java, GeoGebra]
- PLL: Apollonius' Problem with Two Lines and a Point [Java, GeoGebra]
- PPC: Apollonius' Problem with Two Points and a Circle [Java, GeoGebra]
- PPL: An Elementary Solution [Java, GeoGebra]
- PPL: Apollonius' Problem with Two Points and a Line [Java, GeoGebra]
- Prasolov's Pythagorean Identity
- Praying Eyes Theorem [JavaScript, GeoGebra]
- Problem 1 from the 2006 IMO
- Problem 1 from the EGMO2017
- Problem 1 from the Ninth Nordic Mathematical Contest (1994)
- Problem 11984 From the American Mathematical Monthly
- Problem 3 from the EGMO2017
- Problem 4 from the 1959 IMO: Construction of a Right Triangle [Java, GeoGebra]
- Problem 4, 1975 USA Math Olympiad and the Radical Axis [Java]
- Problem 4, 1975 USA Math Olympiad and Isosceles Triangles [Java]
- Problem 4, 1975 USA Math Olympiad: Normals and Tangents [Java]
- Problem 4, 1975 USA Math Olympiad: Problem 4, 1975 USA Math Olympiad: The Final Touch [Java]
- Problem 4 from the 2016 OBJM TST
- Problem 4 from the IMO 2009
- Problem 4 from the 4th BJMO Team Selection Test
- Problem 4087 from Crux Mathematicorum
- Problem 4096 from Crux Mathematicorum
- Problem in an Equilateral Triangle [Java]
- Problem 4 from the IMO 2013 - Synthetic Solution [Javacript, GeoGebra]
- Problem 4160 from the Crux Mathematicorum
- Problem A-2 from the 2002 Putnam Math Competition
- Problem A-6 from the 1992 Putnam Math Competition
- Problem CC156 From Crux Mathematicorum
- Problem in a Special Trapezoid
- Problem in an Equilateral Triangle II [Java]
- Problem in Direct Similarity [JavaScript, GeoGebra]
- Problem in Three Squares [Java]
- Problem of Equal Steps [Java]
- Problem of Equal Steps II [Java]
- Problem on a Pentagonal Star
- Problem with angle bisector from 1975 Canadian Mathematical Olympiad
- Problem with equal angles from 1987 IberoAmerican Mathematical Olympiad
- Proclivity of Conjoint Archimedean Twins for Proliferation [JabvaScript, GeoGebra]
- Projections of Convex Quadrilateral [JavaScript, GeoGebra]
- Projections of Isogonal Conjugate are Concyclic [JavaScript, GeoGebra]
- Projections on Internal and External Angle Bisectors [Java]
- Projective Collinearity in a Quadrilateral [Java]
- Projective infinity
- Projective Invariants for Pascal And Desargues
- Properties of Flank Triangles
- >Two Properties of Flank Triangles - First Proof by Symmetric Rotation [Java, GeoGebra]
- Properties of Flank Triangles - Second Proof by Symmetric Rotation [Java, GeoGebra]
- Properties of Flank Triangles - Proof with an Asymetric Rotation [Java, GeoGebra]
- Two Properties of Flank Triangles - A Proof with Complex Numbers [Java, GeoGebra]
- Two Properties of Flank Triangles - and a Third One [Java, GeoGebra]

- Properties of the Circle of Similitude [Java]
- Properties of Circle Through the Incenter
- Properties of the Figures in Euclid I.47
- Properties of the Harmonic Ratio
- Property of 6-Parpolygon [Java]
- Property of Angle Bisectors [Java]
- Angle Bisector Theorem
- Property of Angle Bisectors II [Java]
- Property of Angle Bisectors III [Java, GeoGebra]
- Property of Internal Angle Bisector - Hubert Shutrick's PWW [Java, GeoGebra]

- Property of Circumscribed Quadrilaterals [Java]
- Property of Points Where In- and Excircles Touch a Triangle [Java]
- Property of Right Isosceles Triangle [Java, GeoGebra]
- Property of Right Trapezoids [GeoGrebra]
- Property of Semicircles [Java]
- Property of Thébault Circles [JavaScript, GeoGebra]
- Property of Two Pencils of Parallel Lines
- Proportions and the Incenter [JavaScript]
- Proportions in Square
- Proportions with Two Orthocenters [JavaScript, GeoGebra]
- Ptolemy's Theorem
- Pure Angle Chasing [JavaScript, GeoGebra]
- Pure Angle Chasing II [JavaScript, GeoGebra]
- Pure Angle Chasing III [JavScript, GeoGebra]
- Puzzles on graphs.
- Pythagorean Theorem (121 proofs)
- A Neglected Pythagorean-Like Formula
- An Extra Illustration of J. E. Bottcher's Proof of the Pythagorean Theorem [Java]
- Huygens' proof
- More Trigonometric Proofs of the Pythagorean Theorem
- Pythagorean Theorem : A Variant of Proof by Tessellation
- Pythagorean Theorem by Hinged Dissection
- Pythagorean Theorem by Hinged Dissection I
- Pythagorean Theorem by Hinged Dissection II
- Pythagorean Theorem from the Shoelace Formula
- Pythagorean Theorem via an Isosceles Triangle [Java]
- False Proofs of the Pythagorean Theorem
- Pythagoras' from Bottema's [Java]
- Pythagoras' Theorem By Sheer Shearing [Java]
- Pythagoras' Theorem By Similarity [Java]
- Pythagoras' Theorem Solely By Sliding [Java]
- Pythagorean Condition in An Isosceles Right Triangle [Java]
- Pythagorean Theorem: J. Adams' Proof by Dissection [Java]
- Pythagorean Theorem: Subtle Dangers of Visual Proof [Java]
- Pythagorean Theorem By Plane Tessellation [Java]
- Pythagorean Theorem, Generalizations of
- Pythagorean Theorem in an Orthodiagonal Quadrilateral [Java]
- Pythagorean Theorem is Equivalent to Parallel Postulate.
- Pythagorean Theorem: Versluys' Proof by Dissection [Java]
- Mechanical Proof of the Pythagorean Theorem
- "Extra-geometric" proofs of the Pythagorean Theorem
- D. Houston's proof: Is it trigonometric?
- Pythagoras' from Broken Chords
- Pythagoras' from the Star of David
- Pythagorean Theorem: An Algebraic Proof with Three Trapezoids
- Pythagorean Theorem for Reciprocals
- A Proof of the Pythagorean Theorem with Orthocenter and Right Isosceles Triangles
- Pythagorean Theorem via the Area Determinant
- Pythagorean Theorem via Geometric Progression
- Pythagoras, with a Nod to the Carpets Theorem
- Pythagoras, from the Power of a Point - Again
- Pythagorean Theorem via Half-Angle Formulas
- Pythagorean Theorem by Analytic Geometry
- Pythagorean Theorem via Equilateral Triangles
- Pythagorean Theorem through Angles 60 and 120
- Pythagorean Theorem Through Three Right Isosceles Triangles
- Pythagorean Theorem through a Rearrangement of a Parallelogram
- Pythagorean Theorem by Stretching

- Pythagorean Perimeter Theorem
- Pythagoras and Vecten Break Japan's Isolation [Java]
- Pythagorean Triples [Java]
- Quadrature: A Child's Play
- Quadrilateral from a Segment
- Quadrilateral Inequality
- Quadrilateral Inscribed into Parallelogram
- Quadrilateral With Equal Opposite Sides And Angles [Java]
- Quadrilateral with 3 Equal Sides [Java]
- Quadrilaterals Formed by Perpendicular Bisectors [Java]
- Quest for Paragon [Java]
- R and r When G on Incircle
- Radical Axis and Center, an Application [Java]
- Radical Axis of Circles Inscribed in a Circular Segment [Java]
- Radical Center [Java]
- Radius and Construction of a Mixtilinear Circle [Java]
- Radius of a Circle by Paper Folding [Java]
- Random Dot Stereograms [Java]
- The Range of r/R in Triangle with Centroid on the Incircle
- Ratios and Orthogonality in a Triangle - Problem from the 2006 Romania MO
- Rational Points On a Circle
- Rectangle Inscribed in Triangle [JavaScript, GeoGebra]
- Rectified, Halved, Sheared, Eyeballs Still Surprise [JavaScript, GeoGebra]
- Reflection in a Triangle Tangent to Parabola [JavaScript, GeoGebra]
- Reflection In Line [Java]
- Reflection in the Circumcenter
- Reflections in Ellipse [Java]
- Reflections of a Line Through the Orthocenter [Java]
- Reflections of a Point on the Circumcircle [Java]
- Reflections of the Orthocenter
- Reflections of the Orthocenter [Java]
- Reflections of the Orthocenter II
Regular Hexagon and Triangle Joined at Vertex [JavaScript, GeoGebra] - Regular Hexagon from Arbitrary Triangle [JavaScript, GeoGebra]
- Regular Octagon by Paper Folding
- Regular Polygons in a Triangular Grid [Java]
- Regular Polyhedra - Platonic Solids
- Tetrahedron [Java]
- Octahedron [Java]
- Cube [Java]
- Icosahedron [Java]
- Dodecahedron [Java]
- Cube In Octahedron [Java]
- Octahedron In Cube [Java]
- Icosahedron In Cube [Java]

- Other Solids
- Regular Pentagon Inscribed in Circle by Paper Folding
- Regular polyhedra and Euler's Theorem
- Reim's Similar Coins I
- Reim's Similar Coins II
- Reim's Similar Coins III
- Reim's Similar Coins IV
- Relation Engendered By Altitudes
- Relation Engendered By Medians
- Relations in a Cyclic Polygon
- Remarkable Line in a Quadrilateral [Java]
- Remarkable Line in Cyclic Quadrilateral [Java]
- Rendezvous [Java]
- Reverse Spoke Illusion [Java]
- Revolving Circles Illusion [Java]
- Rhombus in a Cyclic Quadrilateral [Java]
- Rhombus in Circles [Java, GeoGebra]
- Riemann Sphere and Möbius Transformation
- Surprise: Right Angle in Circle [JavaScript, GeoGebra]
- Surprising Length Dependence In Equilateral Triangle by Miguel Ochoa Sanchez
- Right Triangles on Sides of a Square [Java]
- Rotating Top Illusion [Java]
- Rotating Gears [Java]
- Rotation Transform [Java]
- Product of Rotations [Java]
- Rotations in Disguise [Java]

- Rouse Ball's Fallacy [Java]
- Rusty Compass Construction of Equilateral Triangle [Java]
- Salinon: From Archimedes'
*Book of Lemmas*[Java] - Sam Loyd's Geometric Puzzle
- Sam Loyd's Son's Dissection [Java]
- Sanchez's Areas in Bottema's Configuration [JavaScript]
- Sangaku: Reflections and the Phenomenon
- Sangaku: Critique of My View and a Response
- Sangaku and The Egyptian Triangle
- Sangaku in a Square
- Sangaku Iterations, Is it Wasan? [Java]
- Sangaku via Peru
- Sangaku with 8 Circles
- Sangaku with Angle between a Tangent and a Chord [Java]
- Sangaku with Quadratic Optimization
- Sangaku with Three Mixtilinear Circles [Java]
- Sangaku with Versines [Java]
- Sangakus with a Mixtilinear Circle [Java]
- Scintillating Grid Illusion [Java]
- Schwarz Lantern [Java]
- Secant Angles [Java]
- Secant Angles II [Java]
- Secant, Normal, Tangent [Java]
- Secant, Tangents and Orthogonality [Java]
- See-Saw Lemma [Java]
- Segment Projections in Equilateral Triangle
- Segment Trisection [Java]
- Segment Trisection II
- Segment Trisection Induced by Parallels to Medians [Java]
- Semicircle on Square [JavaScript]
- Semi-regular Tessellation on Hinges A [Java]
- Semi-regular Tessellation on Hinges B [Java]
- Separating point sets with a circle
- Sequences of Concyclic Points on a Conic
- Sequences of Touching Circles
- Serendipitous Beauty [Java]
- Serendipitous Proofs Of The Pythagorean Theorem
- Seven and the Eighth Circle Theorem
- Seven Circles Theorem [Java]
- Seven Concyclic Points [Java, GeoGebra]
- Seven Equal Circles [JavaScript, GeoGebra]
- Seven Problems in Equilateral Triangle
- Seven Problems in Equilateral Triangle, Solution to Problem 1
- Seven Problems in Equilateral Triangle, Solution to Problem 2
- Seven Problems in Equilateral Triangle, Solution to Problem 3
- Seven Problems in Equilateral Triangle, Solution to Problem 4
- Seven Problems in Equilateral Triangle, Solution to Problems 5, 6, 7

- Seyran Ibrahimov's Inequality
- Shaggy Dog Theorem
- Shapes in a lattice
- Shapes of constant width [Java]
- Shearing and Translation in Pythagorean Pants [Java]
- Shearing a Polygon into a Triangle of Equal Area [Java]
- Shearing Butterflies in Quadrilaterals [Java]
- Shedding Light on the Ball for Eyeballing
- Shepard's Parallelogram Illusion [Java]
- Shifted by the Inradius Tangent Collinearities [JavaScript, GeoGebra]
- Shifting Cube Illusion [Java]
- Shimmer Illusion [Java]
- Short Construction of the Geometric Mean
- Shortest Fence in a Quarter-Circle Pasture
- Shredding the torus
- Sides and Area of Pedal Triangle
- Sierpinski Gasket By Common Trema Removal [Java]
- Sierpinski Gasket Via Chaos Game [Java]
- Sierpinski Gasket by Trema Removal [Java]
- Similar Parallelograms on Sides of a Triangle
- Similar Triangles And More
- Similar Triangles in Crossing Circles [JavaScript, GeoGebra]
- Similar Triangles on Sides of a Quadrilateral [Java]
- Similar Triangles on Sides and Diagonals of a Quadrilateral [Java]
- Similarity Is About Proportion - And Ways to Look at It
- Simple Construction of the Circle of Apollonius
- Simple dissection of an acute triangle
- Simple Property of Circle Through the Incenter [JavaScript]
- Simple Quadrilaterals Tessellate the Plane [Java]
- Simson Line [Java]
- Simsons and 9-Point Circles in Cyclic Quadrilateral [Java]
- Simultaneous Contrast Illusion [Java]
- Simultaneous Contrast Illusion II [Java]
- Simultaneous Contrast: Koffka's Illusion [Java]
- Simultaneous Contrast: White's Illusion [Java]
- Simultaneous Contrast: White's Illusion, V-Variant [Java]
- Three Concurrent Chords at 60 Degrees Angles
- Simultaneous Diameters in Concurrent Circles [Java]
- Simultaneous Generalization of the Theorems of Ceva and Menelaus
- Sine and Cosine of 15 Degrees Angle
- Sine, Cosine, and Ptolemy's Theorem
- Six Circles with Concurrent Pairwise Radical Axes
- Six Circles Theorem (Bui Quang Tuan) [Java]
- Six Circles Theorem (Elkies) [Java]
- Six Circles Theorem (Evelyn) [Java]
- Six Concyclic Circumcenters in Fermat's Configuration [JavaScript, GeoGebra]
- Six Concyclic Points [Java]
- Six Concyclic Points on Sides of a Triangle
- Six Concyclic Points II [Java]
- Six Concyclic Points via Antipedal Triangle [JavaScript, GeoGebra]
- Six Incircles in an Equilateral Triangle [Java]
- Six Point Circle [Java]
- SixPoints, ThreeLines [Java]
- Soddy Circles and David Eppstein's Centers [Java]
- Some Properties of Common Tangents [JavaScript, GeoGebra]
- Some Properties of Napoleon's Configuration [Java]
- Spectral Decomposition of a Planar Quadrilateral
- Spectral Decomposition of a Planar Quadrilateral: an Illustration [JavaScript, GeoGebra]

- Sperner's Lemma [Java]
- Spiral Similarity [Java]
- Spiral Similarity and CollinearitySpiral Similarity and Collinearity [Java, GeoGebra]
- Spiral Similarity Leads to Equilateral Triangle [JavaScript, GeoGebra]
- Square and Circle in a Gothic Cupola
- Square from Four Points, One on Each Side
- Solution 1 [Java, GeoGebra]
- Solution 2 [Java, GeoGebra]

- Square From Nowhere [Java]
- Square in a Circle Inscribed in a Square [Java]
- Square in a Right Triangle [Java]
- Square in Chair [Java]
- Square Inscribed in a Triangle [Java]
- Square Inscribed in a Triangle II [Java]
- Square, Similarity and Slopes [Java]
- Squares and Straight Tetrominoes
- Squares in Circles [Java]
- Squares in Semicircle and Circle
- Squares in Triangles
- Squares Inscribed In a Triangle III [Java]
- Squares on Sides of a Parallelogram [JavaScript, GeoGebra]
- Squares on Sides of a Quadrilateral [Java]
- Squares on Sides of a Quadrilateral II [JavaScript, GeoGebra]
- Square out of a Quadrilateral
- Squaring a circle
- Squaring a Rectangle [Java]
- Squinting Eyes Theorem [Java]
- SSA
- SSS
- Staircase Illusion [Java]
- Stan Fulger's Observation in Right Triangle
- Star of David [Java]
- Stathis Koutras' Butterfly
- Stathis Koutras' Theorem
- Stathis Koutras' Theorem II
- Steiner's Circumellipse in Barycentric Coordinates [GeoGebra]
- Steiner's Inellipse
- Steiner's Sangaku
- Steiner's Ratio Theorem
- Steiner's Theorem
- Stereographic Projection [Java]
- Stereographic Projection and Inversion
- Stereographic Projection and Radical Axes
- Stewart's theorem
- Straight Edge Only Construction of Polar
- Structural Constellation [Java]
- Sums of Squares in Circle
- Sum of Squares in Equilateral Triangle
- Sum of Squares of Distances to Vertices
- Sum of Two Squares [JavaScript, GeoGebra]
- Sums of Unit Vectors
- Surprising 60° in Equilateral Triangle [JavaScript, GeoGebra]
- Sylvester's Problem
- Symmedians
- Symmedian and Antiparallel [Java]
- Symmedian and 2 Antiparallels [Java]
- Symmedian and the Tangents [Java]
- Symmedian in a Right Triangle [Java]
- Symmedian in Right Triangle II [JavaScript, GeoGebra]
- Symmedian via Squares and a Circle
- Symmedian and the Simson [JavaScript, GeoGebra]
- Symmedian via Parallel Transversal and Two Circles [JavaScript, GeoGebra]

- Symmetries in a Triangle
- Symmetries in Triangle II [JavaScript, GeoGebra]
- Symmetry in an Asymmetric Configuration [JavaScript, GeoGebra]
- (tan(72°)±tan( 60°)sin(30°$\mp$18°)= 1
- Tangency Point of Two Circles [Java]
- Tangent and Secant [Java]
- Tangent as a Radical Axis [Java]
- Tangent Circles, Similarity and Equal Segments [JavaScript, GeoGebra]
- Tangent Circles and an Isosceles Triangle [Java]
- Tangent Circles in a Parallelogram [Java]
- Tangent, Cotangent and Square Roots Inequality
- Tangent Curiosity in Equilateral Triangle [JavaScript, GeoGebra]
- Tangent in Concurrency [Java]
- Tangent Lines and Circles in Convex Quadrilateral [Java]
- Tangent of 22.5° - Proof Wthout Words
- Tangent to Circle in Three Steps
- Tangent to the Incircle [JavaScript]
- Tangent to two circles
- Tangents And Bisectors
- Tangents and Diagonals in Cyclic Quadrilateral [Java]
- Tangents, Perpendiculars and Geometric Mean [Java]
- Tarski-Banach Decompositions
- Taylor circle [Java]
- Terquem's Theorem [Java]
- Tesseract [Java]
- Tetrahedron in Parallelepiped
- Tetrahedron with Equiareal Faces
- Tetrahedron with Equiareal Faces, II
- Tetrahedron with Orthogonal Perpendiculars to Opposite Edges
- Thales' Theorem [Java, GeoGebra]
- Thales' Theorems
- Thales on Angle Bisectors [JavaScript, GeoGebra]
- The 80-80-20 Triangle
- 1 Solution to a modified problem with angles of 40° and 50°.
- 2 Solutions to a modified problem in the 80-80-20 triangle
- 8 Solutions to a derivative problem in the 80-80-20 triangle
- 10 Solutions to the classical problem in the 80-80-20 triangle
- The 80-80-20 Triangle Problem, Solution #12
- The 80-80-20 Triangle Problem, A Variant
- The 80-80-20 Triangle Problem, 20-30 case

- The Beauty of Fractions
- The Center of Gravity and Motion of Material Points [JavaScript, GeoGebra]
- The Chaos Game: Address Space vs IFS [Java]
- The Devil is in the Exceptions
- The Eutrigon Theorem [Java, GeoGebra]
- The Eutrigon Theorem [JavaScript, GeoGebra]

- The Golden Pentacross
- The Law of Cosines by Larry Hoehn
- The Midpoint of an Angle Bisector - a Problem by A. A. Zaslavsky
- The only rational triangle
- The Pythagorean Theorem from a Combinatorial Identity
- The Schwarz Lantern Explained [JavaScript]
- The Shape of the Colosseum [Java, GeoGebra]
- The Shortest Crease [JavaScript, GeeoGebra]
- Thébault's Problem I [Java]
- Thébault's Problem II [Java]
- Thébault's Problem III [Java]
- The Triangle of the Medians
- Theorem of Complete Quadrilateral [Java]
- Theorem of Three Tangents to a Conic [JavaScript, GeoGebra]
- Theorems of Ceva and Menelaus, an Illustrated Generalization [Java]
- There is no Difference Between Equilateral Triangles
- Third Unusual Identity in Triangle
- Three Circles and Area [JavaScript]
- Three Circles and Common Tangents
- Three Circles through the Incenter
- Three Collinear and Four Concyclic Points [Java, GeoGebra]
- Three Concurrent Circles [Java]
- Three Common Chords in Three Concurrent Circles [Java, GeoGebra]
- Three Congruent Circles by Reflection [Java]
- Three Congruent Circles by Reflection II [Java]
- Three Congruent Circles by Reflection III [Java]
- Three Equal Circles in a Semicircle
- Three Euler Lines That Are Four [JavaScript]
- Three Incircles In a Right Triangle [Java]
- Three Incircles in a Triangle [Java]
- Three Isosceles Triangles [Java]
- Three Orthogonal Circles Through Three Given Points [Java]
- Three lines at 60 degres and Circumcenters [JavaScript, GeoGebra]
- Three pairs of Parallel Lines and a Conic [JavaScript, GeoGebra]
- Three Parabolas with Common Directrix [JavaScript,GeoGebra]
- Three Parallels in a Triangle [Java]
- Three Points on a Parabola [Java]
- Three Pyramids are Better Than Two [Java]
- Three regions sharing a common boundary
- Three Similar Polygons [Java]
- Three Similar Triangles [Java]
- Three Similar Triangles II [Java]
- Three Squares and Two Ellipses [Java]
- Three Tangent Circles [Java]
- Three Tangents, Three Chords in Ellipse [Java]
- Three Tangent Circles Sangaku
- Three Tangents Theorem [Java]
- Three Tangents, Three Secants [Java]
- Three Touching Circles [Java]
- Three Travelers in Uniform Motion
- Three visions of a fact [GeoGebra]
- Tiling a Chessboard with Dominoes
- Tiling Sphere by Four Equal Triangles
- Toothpick Construction of a Square [Java]
- Topological preliminaries
- Torque as a Mathematical Object
- Touching Circles [Java]
- Touching Circles and Concurrency [Java]
- Touching Circles with Given Centers II [Java]
- Train wheel quandary
- Transitivity in Action [Java]
- Translated Triangles [Java]
- Translation Transform [Java]
- Transversal Trigonometry [JavaScript, GeoGebra]
- Triangle ABC is right iff sin²A + sin²B + sin²C = 2
- Triangle Area in Square with Incircle
- Triangle Areas in a Parallelogram [Java]
- Triangle Areas in a Parallelogram II [Java]
- Triangle by HM segments [JavaScript, GeoGebra]
- Triangle Classification [Java]
- Triangle constructions and facts [Java]
- Triangle Construction from Angle, Altitude and Median
- Triangle from a, A, m
_{c}/m_{b} - Triangle from Angle Bisector, Altitude and Circumradius
- Triangle from Angle Bisector, Altitude and Inradius
- Triangle from Inradius, Circumradius, Side or Angle
- Triangle from Median, Altitude and Circumradius
- Triangle from Side, Circumradius, and Median
- Triangle from Angle, Inradius, and Difference of Sides
- Triangle from Side, Inradius, and Altitude
- Triangle from Side, Median, and Altitude
- Triangle from Two Side Lines and the Euler Line
- Triangle in a 4x4 Square
- Triangle in a 5x5 Square
- Triangle of Maximum Area
- Triangle of Maximum Area II
- Triangle of Minimum Perimeter [JavaScript]
- Triangle on a Rectangular Hyperbola
- Triangle Sliding on Two Straight Lines [Java]
- Triangles, Squares and Areas from Temple Geometry [Java]
- Triangles on HO
- Triangles with Equal Area [Java]
- Triangles with Sides in Geometric Progression [JavaScript]
- Triangular Areas in Circle [JavaScript, GeoGebra]
- Triangular Billiard [Java]
- Triangulating Squares
- Triangle with a 60 degrees angle [JavaScript, GeoGebra]
- Trigonometry by Watching
- Trigonometric Form of Ceva's Theorem [Java]
- Trigonometric Functions [Java]
- Trigonometric Identities with Arctangents
- Trigonometric Identity for the Pi Day
- Trigonometric Proof of the Pythagorean Theorem
- Trigonometry According to Ptolemy
- Trigonometry by Paper Folding
- Trisect Segment: 2 Circles, 4 Lines
- Trisectable angle that is not constructible
- Tucker Circles [Java]
- Tucker Circles Through Homothety [Java]
- Twelve Matchsticks Area Puzzle
- Twin Segments in Four Semicircles
- Twins Beget Twins
- Twisted Cord Illusion [Java]
- Two Altitudes, One Midpoint
- Two Arbelos, Two Chains
- Two Cevians and Proportions in a Triangle
- Two Circles, Two Segments - One Ratio
- Two Circles and a Limit - Analytic Proof
- Two Circles and One More [Java]
- Two Circles and Two More [Java]
- Two Circles, Ellipse, and Parallel Lines
- Two Circles in a Parallelogram [Java]
- Two Circles Inscribed in a Parallelogram [Java]
- Two Circles in a Square [Java]
- Two Circles in a Square II [Java]
- Two Circles in an Angle [Java]
- Two Circles on Angle Bisector [Java]
- Two Circles on a Side of a Triangle [Java]
- Two Circles, Tangents and Two Collinearities [JavaScript, GeoGebra]
- Two Circumcircles And Two Pairs of Parallels [Java]
- Two Circumcircles in Triangle [Java]
- Two Conditions for a Triangle to Be Equilateral
- Two coins puzzle
- Two Congruent Circles by Reflection [Java]
- Two Conics, Pascal, Chasles, and Cross-Ratio [JavaScript, GeoGebra]
- Two Color Coloring of the Plane [Java]
- Two Common Chords in Three Concurrent Circles [Java, GeoGebra]
- Two Diameters and Longest Common Chord [Java, GeoGebra]
- Two Equilateral Triangles [Java]
- Two Equilateral Triangles on Sides of a Square
- Two Homotheties in a Parallelogram [Java]
- Two Intersecting Circles [Java]
- Two Lines - Two Circles [Java]
- Two Pencils of Parallel Lines [JavaScript, GeoGebra]
- Two Pairs of Parallel Lines in a Triangle [Java, GeoGebra]
- Two Parallels in a Triangle and One More [Java]
- Two Pascals Merge into One [JavaScript, GeoGebra]
- Two Perpendiculars From a Point to a Line [Java]
- Two Planar Constructions Related to a 3D Problem
- Two Perspective Triangles
- Two Quadrilaterals [Java]
- Two Quadruplets of Concyclic Points [JavaSCript,GeoGebra]
- Two Quadruplets of Tangent Circles [Java]
- Two Refinements of Ionescu-Weitzenbock Inequality
- Two Regular Pentagons Joined at Vertex
- Two Related Triangles of Equal Areas
- Two Sangaku with Equal Incircles
- Two Similar Triangles with Parallel Sides [JavaScript, GeoGebra]
- Two Simsons in a Triangle [Java]
- Two Squares and Another Square [Java]
- Two Squares In Circle [JavaScript]
- Two Symmetric Triangles Are Directly Decomposable [Java]
- Two Touching Circles [Java]
- Two Triangles Inscribed in a Conic [Java, GeoGebra]
- Two Triangles Inscribed in a Conic - with Elementary Solution [Java, GeoGebra]
- Two Triangles Inscribed in a Conic - with Solution [Java, GeoGebra]
- Two Triangles With Common Base and Altitude [Java]
- Two Triangles Sharing the Circumcenter
- Two Triples of Concurrent Cevians and a Conic [JavaScript, GeoGebra]
- Two Triples of Concurrent Circles [Java]
- Two Triples of Similar Triangles [Java]
- Uncommon Triangle Constructions
- Unfolding Spirals Illusion [Java]
- Urquhart's Theorem
- USA 1975 Problem 4
- Use of Homogeneous Coordinates for Geometrical Calculations
- Van Aubel's Theorem for Quadrilaterals and Generalization
- Van Khea's Fourth Identity in Triangle
- Van Khea's Quickie
- Van Obel Theorem, Determinants, and Barycentric Coordinates
- Van Schooten's and Pompeiu's Theorems [Java]
- Van Schooten's Locus Problem [Java]
- Variations on the Theme of Tremas [Java]
- Variations on the Theme of Tremas II [Java]
- Varignon's Theorem, Proof Without Words
- Varignon Parallelogram [Java]
- Various Geometries
- Vecten-Nikolin Hexagon [Java]
- Vecten's Collinearity [Java]
- Vecten's Mesh [Java]
- Vector Addition and Subtraction [Flash]
- Vector Algebra in Tetrahedron
- Vector product
- Versatile Theorem [Java]
- Vertical and Horizontal Dominoes on a Chessboard
- Vietnamese Extension of a Japanese Theorem [JavaScript]
- Vietnamese Lemma towards an Extension of a Japanese Theorem [JavaScript, GeoGebra]
- Viewing a Statue
- Viviani's Theorem [Java]
- Slanted Viviani [JavaScript,GeoGebra]
- Slanted Viviani, PWW [JavaScript, GeoGebra]
- Tony Foster's Proof of Viviani's Theorem

- Viviani's Theorem II [Java]
- Viviani in Isosceles Triangle [Java]
- Viviani by Inversion
- Viviani by Vectors
- Viviani's 3D Analogue
- Sanchez's Viviani's Area Analogue [JavaScript, GeoGebra]
- Volume and Area of Torricelli's Trumpet [JavaScript]
- Volume of Fibonacci Tetrahedron
- Volume of Sphere and Volume of an Ellipsoid
- Volumes of Two Pyramids
- Wallace-Bolyai-Gerwien Theorem
- Wallace's Theorem [Java]
- Watt's and Chebyshev's Linkage [Java]
- Weird curves bound normal areas
- Weitzenbock by Sanchez
- Weitzenböck Inequality [Java]
- What does one see inside a spherical mirror? [Java]
- What Is Analytic Geometry?
- What Is Angle?
- What Is Angle Chasing?
- What Is Area?
- What Is Ellipse?
- What Is Indirect Proof?
- What Is Line?
- What Is Point?
- When a Triangle is A-cute
- When a Triangle is Equilateral [Java]
- When Is Triangle Equilateral: Marian Dinca's Criterion
- When Is Triangle Isosceles: Miguel Ochoa Sanchez's Criterion
- When Two Segments Intersect? [JavaScript]
- When index equals content [Java]
- Wonderful Trigonometry In Equilateral Triangle
- Why a Diameter Is the Longest Chord?
- William Wallace's Proof of the Butterfly Theorem
- William Wallace's 1803 Statement of the Butterfly Theorem [JavaScript, GeoGebra]
- Wittenbauer's Parallelogram [Java]
- Wundt Illusion [Java]
- Wundt Block Illusion [Java]
- Y. Sawayama's Lemma [Java]
- Y. Sawayama's Theorem
- YATPOPT, Yet Another Trigonometric Proof of the Pythagorean Theorem
- Yet Another Appearance of the Golden Ratio [JavaScript, GeoGebra]
- Yet Another Concurrence on the 9-Point Circle [JavaScript, GeoGebra]
- Yet Another Seven Circles Theorem [JavaScript, GeoGebra]
- Zaslavsky's theorem [Java]
- Zöllner's Illusion [Java]

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