Geometry articles, theorems, problems

What Is Geometry?
What Is Analytic Geometry?

Pictorial Geometry Index

  1. 1 + 27 = 12 + 16 Sangaku
  2. 120° Breeds 90° [Java]
  3. 3-4-5, Golden Ratio
  4. 3 Roads, 3 Travelers [Java]
  5. 3 Utilities Puzzle
  6. 3D Concurrency Of Altitudes
  7. 3D Quadrilateral - a Coffin Problem
  8. 3-4-5 Triangle by a Kid
  9. 4 Travelers problem
  10. 5-Step Construction of the Golden Ratio, One of Many
  11. 5x5 Square Grid and 5 Circes [Java, GeoGebra]
  12. 6 to 9 Point Circle [Java]
  13. 60° Angle And Importance of Being The Other End of a Diameter
  14. 60o Breeds 90o [Java]
  15. 7 = 2 + 5 Sangaku
  16. 9-point Circle as a Locus of Concurrency [Java]
  17. 9 Point Center on Angle Bisector [GeoGebra]
  18. A 60° Rhombus in a 60° Isosceles Trapezoid
  19. A better solution to a difficult sangaku problem
  20. A Case of Similarity [Java]
  21. A Chain of Touching Circles in a Polygon (a la Bui Quang Tuan) [Java]
  22. A Chain of Touching Circles in a Polygon (à la Evelyn) [Java]
  23. A Characterization of the Euler Line [Java]
  24. A Circle in an Isosceles triangle from the 2006 Irish MO
  25. A Circle Related to Incenter and Circumcenter [Java]
  26. A Circle Rolling in an Equilateral Triangle [Java]
  27. A Circle With Two Centers [Java]
  28. A Conic in a Triangle [JavaScript, GeoGebra]
  29. A Combinaton Locus
  30. A Corrected Version of the Calculus Proof of the Pythagorean Theorem
  31. A Curious Identity in Triangle
  32. A Cyclic Inequality in Triangle
  33. A Cyclic Inequality in Triangle II
  34. A Cyclic Inequality in Triangle for Integer Powers
  35. A Degenerate Case of Bottema's Configuration [Java, GeoGebra]
  36. A Diameter As a Diagonal of Inscribed Quadrilateral [Java, GeoGebra]
  37. A Discovery of Hirotaka Ebisui And Thanos Kalogerakis
  38. A dissection puzzle. Proof #99 of the Pythagorean theorem
  39. A Double Meaning of an Arc's Midpoint [Java, GeoGebra]
  40. A Family of Cyclic Quadrilaterals [JavaScript, GeoGebra]
  41. A Generalization of Simson Line [JavaScript, GeoGebra]
  42. A Generalization of the Pythagorean Theorem
  43. A Generalization of Van Aubel's Theorem
  44. A Generalized Cavalieri-Zu Principle
  45. A Geometric Limit
  46. A Geometry Problem from 2012 IMO - Problem 5
  47. A Hard but Important Sangaku
  48. A Hinged Realization of a Plane Tessellation [Java]
  49. A Lemma of Equal Areas [Java]
  50. A Lemma on the Road to Sawayama
  51. A Line in a Square Grid [Java]
  52. A Line in Triangle Through the Circumcenter [Java]
  53. A Matter of Collinearity: Metamorphosis of a Problem
  54. A Modified Sangaku
  55. A Multiplicative Identity of Areas in a Triangle [Java]
  56. A Note on Cavalieri's Indivisibles
  57. A Parallelogram in Triangle [Java]
  58. A Plane Filling Curve for the Year 2017
  59. A Possibly First Proof of the Concurrence of Altitudes
  60. A Problem from Greece via Peru
  61. A Problem from the 1985 Balkan Mathematical Olympiad (Shortlist)
  62. A Problem in a Configuration of Three Squares
  63. A Problem in a Special Tangential Quadrilateral
  64. A Problem In an Isosceles Right Triangle [Java]
  65. A Problem in Pentagon with Right Angles
  66. A Problem in Pentagon with Supplementary Angles
  67. A Problem in Three Pentagons [JavaScript, GeoGebra]
  68. A Problem of Acute Triangle
  69. A Problem of Two Incircles by Miguel Ochoa Sanchez
  70. A Problem on an Icy Cone
  71. A problem with equilateral triangles [Java]
  72. A Problem with Right Isosceles Triangles [JavaScript]
  73. A Problem with Three Equilateral Triangles
  74. A Problem with Two Isosceles Triangles [JavaScript]
  75. A Problem with Two Similar Rectangles
  76. A Proof Perigal and All Others After Him Missed
  77. A Property of a Median [JavaScript, GeoGebra]
  78. A Property of Angle Bisectors
  79. A Property of Circle Through the Incenter [JavaScript]
  80. A Property of Incenter Relative to Circumcircle
  81. A Property of Cyclic Quadrilateral
  82. A Property of Equiangular Polygons [Java]
  83. A Property of Inscriptible Quadrilaterals [JavaScript]
  84. A Property of Isogonal Lines [JavaScript, GeoGebra]
  85. A Property of Orthic Triangle [JavaScript, GeoGebra]
  86. A Property of Pascal's Hexagon Pascal May Have Overlooked
  87. A Property of Perspective Triangles [JavaScript, GeoGebra]
  88. A Property of Points on Excircle
  89. A Property of Points on Incircle
  90. A Property of Rhombi [Java]
  91. A Property of the Line IO [Java]
  92. A Property of the Line IO: A Bundled Statement and Proof [Java]
  93. A Property of the Line IO: a proof from the Book [Java]
  94. A Property of Trapezoid with a Right Angle
  95. A Rectangle in Three Circles by Hirotaka Ebisui
  96. A Relation in Inscribed Tetrahedra
  97. A Relation in Triangle
  98. A Restored Sangaku
  99. A Sangaku Follow-Up on an Archimedes' Lemma [Java]
  100. A Sangaku: Two Unrelated Circles [Java]
  101. A Sangaku with an Egyptian Attachment [Java]
  102. A Sangaku with Many Circles and Some [Java]
  103. A Simple Solution to a Difficult Sangaku Problem
  104. A Special Point: Intersection of the Diagonals in Quadrilateral
  105. A Special Triangle with a Line Through the Lemoine Point
  106. A square in parallel lines
  107. A Straightedge Construction of the Midpoint of a Chord Common to Two Circles
  108. A Stronger Triangle Inequality [Java]
  109. A Sushi Morsel
  110. A Theorem of M. Mansion
  111. A Three Pegs Question [Java]
  112. A Triangle in a Rhombus with a 60 Degrees Angle
  113. A Triangle of Antreas Hatzipolakis [Java]
  114. A Triangle Problem from Caucasus
  115. A Triangle With a 45 Degrees Angle in Square
  116. A Trigonometric Identity in a Right Triangle from the 1960 IMO
  117. A Trigonometric Solution to a Difficult Sangaku Problem
  118. A Two-Triangle Inequality
  119. A Two-Triangle Inequality II
  120. A View on the Circle of Apollonius [JavaScript,GeoGebra]
  121. About a Line and a Triangle [Java]
  122. Abul Wafa al-Buzjani's Proof of the Pythagorean Theorem [Java]
  123. Abutting Equilateral Triangles on a Line I [JavaScript, GeoGebra]
  124. Acute Angle Bisectors in a Right Triangle [Java]
  125. Adams' Circle [Java]
  126. Addition and Subtraction Formulas for Sine and Cosine
  127. Addition and Subtraction Formulas for Sine and Cosine II
  128. Adil Abdulayev's Inequality With Angles, Medians, Inradius and Circumradius
  129. Adil Abdullayev's Inequality With Roots and Powers
  130. Algebraic proof of the theorem of butterflies in quadrilaterals
  131. Algebraic-Geometric Equation
  132. All about altitudes
  133. All Triangles Are Isosceles [Java]
  134. All Trigonometric Inequality in Triangle
  135. Altitudes and the Euler Line [GeoGebra]
  136. Altitudes and the Power of a Point [Java]
  137. Altitudes Concur at a Point: a Second Look
  138. Altitudes have ears, foot, stem, and root
  139. An Affine Property of Barycenter
  140. An Algebraic Lemma with Geometric Consequences [JavaScript]
  141. An All-Inclusive Inequality
  142. An All-Inclusive Inequality II
  143. An Angle in Square Conjoint with Regular Pentagon
  144. An Angle Inequality in Simple Polygons
  145. An Equilateral Triangle In Parallel Lines
  146. An Area Inequality
  147. An Area Inequality in Right Triangle
  148. An Asymmetric Inequality
  149. An Euclidean Construction with Inversion [Java, GeoGebra]
  150. An Extension of a Sangaku with Touching Circles
  151. An Extension of van Schooten's Theorem
  152. An Extra Triple of Equilateral Triangles for Napoleon [JavaScript, GeoGebra]
  153. An Identity for Regular Tetrahedra
  154. An Identity in a Regular Heptagon
  155. An Identity in (Cyclic) Quadrilaterals [JavaScript, GeoGebra]
  156. An Identity in Cyclic Quadrilateral
  157. An Identity in Triangle
  158. An Identity in Triangle II
  159. An Identity in Triangle with a 135 Degrees Angle
  160. An Inequality in Triangle with a Constraint
  161. An Inequality in Triangle with Side Lengths and Circumradius
  162. An Inequality with Exradii and an Altitude
  163. An Identity with Inradius and Circumradii
  164. An Inequality for Sides and Area
  165. An Inequality for the Cevians through Circumcenter
  166. An Inequality for the Cevians through Spieker Point via Brocard Angle
  167. An Inequality from the 2015 Romanian TST
  168. A Cyclic Inequality from the 6th IMO, 1964
  169. A Property of Nagel Cevians
  170. An Inequality in Acute Triangle, Courtesy of Ceva's Theorem
  171. An Inequality in Cyclic Quadrilateral
  172. An Inequality in Cyclic Quadrilateral II
  173. An Inequality in Cyclic Quadrilateral III
  174. An Inequality in Cyclic Quadrilateral IV
  175. An Inequality of the Areas of Triangles Formed by Circumcenter And Orthocenter
  176. An Inequality on Circumscribed Quadrilateral
  177. An Inequality in Triangle
  178. An Inequality in Triangle II
  179. An Inequality in Triangle III
  180. An Inequality in Triangle IV
  181. An Inequality in Triangle, V
  182. An Inequality in Triangle, VI
  183. An Inequality in Triangle XI
  184. An Inequality in Triangle, Mostly with the Medians
  185. An Inequality In Triangle That Involves the Four Basic Centers
  186. An Inequality in Triangle with Altitudes, Medians And Symmedians
  187. An Inequality in Triangle, with Integrals
  188. An Inequality in Triangle with Roots and Circumradius
  189. An Inequality in Triangle, with Sines
  190. An Inequality in Triangle, with Sines II
  191. An Inequality in Triangle with the Circumradius, Inradius and Angle Bisectors
  192. An Inequality in Triangle with the Sines of Half-Angles and Cube Roots
  193. An Inequality Involving Fermat Point
  194. An Inequality Not in Triangle
  195. An Inequality of Degree 3 with Inradius
  196. An Inequality with Altitudes and Angle Bisectors
  197. An Inequality with Altitudes and Medians

    An Inequality with Angle Trisectors

  198. An Inequality with Arctangents in Triangle
  199. An Inequality with Circumradii And Distances to the Vertices
  200. An inequality with Cosines and a Sine
  201. An Inequality with Inradius and Side Lengths
  202. An Inequality with Cotangents And the Circumradius
  203. An Inequality with Tangents and Sides
  204. An Inequality with One Tangent and Six Sines
  205. An inequality with Three Points
  206. An Inequality in Triangle with Differences of the Medians
  207. An Inequality with Inradius and Circumradii
  208. An Inequality in Triangle with the Medians, Sines and Cube Roots
  209. An Inequality with Powers of Six
  210. An Inequality with Sides, Altitudes, Angle Bisectors and Medians
  211. An Inequality with Sides, Cosines, and Semiperimeter
  212. An Inequality with Sin, Cos, Tan, Cot, and Some
  213. An Inequality with Sines
  214. An Inequality with Tangents and Cotangents
  215. An Inequality with the Most Important Cevians
  216. An Inradii Relation in Inscriptible Quadrilateral [JavaScript]
  217. An Isoperimetric Problem in Quadrilateral
  218. An Isoperimetric Theorem [Java]
  219. An Old Japanese Theorem
  220. An Unexpected Pair of Similar Triangles Which Are Equal [JavaScript, GeoGebra]
  221. An Unexpected Rhombus [JavaScript, GeoGebra]
  222. An Universal Inequality for Cevians
  223. An Unusual Generalization of the Pythagorean Theorem
  224. An Unusual Generalization of the Pythagorean Theorem, a Variant
  225. Angle: An Illustrated Classification [Java]
  226. Angle Bisector in Square
  227. Angle Bisectors Cross Circumcircle
  228. Angle Bisector in Equilateral Trapezoid
  229. Angle Bisector in Parallelogram [Java]
  230. Angle Bisectors In Rectangle [Java]
  231. Angle Bisector in Touching Circles [Java]
  232. Angle Bisectors [Java]
  233. Angle Bisectors and Perpendiculars in a Quadrilateral [Java]
  234. Angle Bisectors in Ellipse [Java]
  235. Angle Bisectors in Ellipse II [Java]
  236. Angle Bisectors in a Quadrilateral [Java]
  237. Angle Bisectors in a Quadrilateral - Cyclic and Otherwise [Java]
  238. Angle Bisectors On Circumcircle [Java]
  239. Angle Chasing on Radical Axis [JacaScritp, GeoGebra]
  240. Angle Chasing in a 75-30-75 triangle
  241. Angle in Square
  242. Angle in Right Triangle
  243. An Angle Inequality in Triangle with Perpendicular Medians
  244. Angle Preservation Property [Java]
  245. Angle Subtended by a Diameter [Java]
  246. Angle Trisection, the Impossibility of Thereof
  247. Angle Trisection by Archimedes [Java]
  248. Angle Trisection by Hippocrates [Java]
  249. Angle Trisection by Paul Vjecsner [Java]
  250. Angle Trisectors on Circumcircle [Java]
  251. Angle Trisection by Paper Folding
  252. Angles in 4-5-6 Triangle [JavaScript]
  253. Angles in a Cube I [Java]
  254. Angles in a Cube II [Java]
  255. Angles in a Cube III [Java]
  256. Angles in Triangle Add to 180o
  257. Angles in a Triangle: an Exercise
  258. Angles Inscribed in an Absent Circle [Java]
  259. Another Concurrence on the 9-Point Circle [JavaScript, GeoGebra]
  260. Another Equilateral Triangle in Napoleon's Configuration [JavaScript, GeoGebra]
  261. Another Geometry Problem from 2012 IMO - Problem 1
  262. Another Golden Ratio in Semicircle
  263. Another Identity in Triangle
  264. Another Pair of Archimedean Twins - a Redux [JavaScript, GeoGebra]
  265. Another Property of Points on Incircle
  266. Another Property of the 9-Point Circle [JavaScript, GeoGebra]
  267. Another Refinement of the Ionescu-Weitzenbock Inequality
  268. Another Sangaku in Square
  269. Another Seven Circles Theorem [JavaScript, GeoGebra]
  270. Anticenter and Orthocenters [JavaScript, GeoGebra]
  271. Anticomplementary Triangle Surprise [Java]
  272. Antiparallel [Java]
  273. Antiparallel and Circumradius [JavaSCript, GeoGebra]
  274. Antiparallel via Three Reflections [Java]
  275. APMO 1995 Problem 3
  276. APMO 1998, Problem 4
  277. APMO 2002, Problem 3
  278. APMO 2003, Problem 2
  279. APMO 2004, Problem 2
  280. The Averages of Sides and Angles in a Triangle
  281. The Problem of Apollonius
  282. Approximate Construction of Regular Pentagon by A. Dürer
  283. Arbelos -- the Shoemaker's Knife [Java]
  284. Another Pair of Twins in an Arbelos [Java]
  285. Archimedes' Quadruplets [Java]
  286. Archimedes' Twin Circles and a Brother [Java]
  287. Area and Perimeter of Circle
  288. Area Inequalities in Triangle
  289. Area Inequality in Three Triangles
  290. Area of an Arbelos [Java]
  291. Area of Cevian Triangle
  292. Area of Cutoff Triangles
  293. Area of Rectangle
  294. Area of the Intersection of Two Equal Rectangles [JavaScript, GeoGebra]
  295. Area of Trapezoid
  296. Area Optimization in Trapezoid
  297. Area, Sector Area, and Segment Area of an Ellipse
  298. Areas between Two Parallelograms [JavaScript, GeoGebra]
  299. Areas in Three Squares [JavaScript, GeoGebra]
  300. Average Distance to N Points
  301. Chain of Circles on a Chord [Java]
  302. Chain of Four Intersecting Circles [JavaScript, GeoGebra]
  303. Chain of Inscribed Circles [Java]
  304. Chain of Six Intersecting Circles [JavaScript, GeoGebra]
  305. Characterization of the Symmedian Point with Medians and Orthic Triangle
  306. Characterization of Trapezoid [JavaScript, GeoGebra]
  307. Chasing Secant Angles [JavaScript]
  308. Concurrence in Arbelos [JavaScript, GeoGebra]
  309. Concurrency in Arbelos [Java]
  310. Concurrence on Angle Bisector [JavaScript, GeoGebra]
  311. Concurrent Chords in a Circle, Equally Inclined
  312. Concyclic Points in Arbelos [Java]
  313. Rectangle in Arbelos [Java]
  314. Rectangular Areas in Circle [JavaScript, GeoGebra]
  315. Red and Pink Areas
  316. Reuleaux's Triangle, Extended [GeoGebra]
  317. Small Triangle from Small Triangle
  318. Square, 45 Degrees Angle and Pythagoras' Look-alike
  319. Square, Semicircle, and Other Curves [JavaScript, GeoGebra]
  320. Squares in Arbelos [Java]
  321. Twin Segments in Arbelos [Java]
  322. Archimedean Siblings out of Wedlock, i.e., Arbelos (JavaScript, GeoGebra)
  323. Archimedes'Book of Lemmas
  324. Arbelos' Morsels [JavaScript, GeoGebra]
  325. Archimedes' Law of the Lever [Java]
  326. Archimedes' Method
  327. Archimedes' Twins in the Edo Period
  328. Area and Perimeter Splitters in a Triangle
  329. Area Inequality in Trapezoid
  330. Area Inequality in Triangle
  331. Area Inequality in Triangle II
  332. Area of a Bicentric Quadrilateral
  333. Area of a Circle by Leonardo da Vinci [Java]
  334. Area of a Circle by Rabbi Abraham bar Hiyya Hanasi [Java]
  335. Area of Isosceles Triangle
  336. Area of Median Triangle [Java]
  337. Area of Parallelogram [Java]
  338. Area of Parallelogram Formula by Shearing
  339. Area of the Union of Two Squares [Java]
  340. Area of Triangle [Java]
  341. Areas and Centroid in a Triangle [Java]
  342. Areas In Circle
  343. Areas in Square by Dissection [Java]
  344. Areas in Two Parallelograms and a Translation [JavaScript, GeoGebra]
  345. Arithmetic-Geometric Mean Inequality
  346. Arithmetic Mean Sangaku [Java]
  347. Arithmetic Mean Sangaku II [Java]
  348. Around the Incircle [Java]
  349. Around the Incircle in a Polygon [Java]
  350. Artisans vs Mathematicians
  351. Asian Pacific Kite [Java]
  352. Assigning Numbers to Points in the Plane
  353. Assimilation Illusion [Java]
  354. Axis of Similitude of Three Circles
  355. Barbier, The Theorem of [Java]
  356. Barycenter of Cevian Triangle
  357. Barycentric coordinates
  358. Batman's Problem [JavaScript, GeoGebra]
  359. Bender: A Visual Illusion [Java]
  360. Bespectacled Eyeballs Extension [JavaSCript, GeoGebra]
  361. Between a Cross and a Square (lies a Golden Ratio)
  362. Between Major and Minor Circles [Java]
  363. Bevan's Point and Theorem [Java]
  364. Beyond Pythagoras
  365. Beyond Viviani [JavaScript]
  366. Bimedians and Diagonals in a Quadrilateral
  367. Bimedians in a Regular Tetrahedron [Java]
  368. Bisectal Circle [Java]
  369. Bisecting arcs
  370. Bisecting a shape
  371. Bisection of Yin and Yang
  372. Bisector of an imaginary angle may be real
  373. Bisectors and Proportions [JavaScript]
  374. BMO 2014, Problem 3 [JavaScript, GeoGebra]
  375. Bottema Shatters Japan's Seclusion [Java]
  376. Bottema's theorem [Java]
  377. Bottles in a Wine Rack [Java]
  378. Bounded Distance
  379. Bounds for the Sum of Distances to the Vertices [JavaScript]
  380. Brahmagupta's Formula and Theorem
  381. Brahmagupta's Theorem [Java]
  382. Brahmagupta-Mahavira Identities
  383. Brianchon in Ellipse [Java]
  384. Brianchon's theorem [Java]
  385. Brick Wall Illusion [Java]
  386. Bride's Chair [Java]
  387. Brief introduction to Rational Trigonometry
  388. Brocard Point and a Relation of Circumradii
  389. Broken Chord Theorem [Java]
  390. Broken Line in Triangle
  391. Building a Bridge [Java]
  392. Building Bridges [Java]
  393. Bulging lines illusion [Java]
  394. Butterfly Theorem
  395. Cabart's Collinearity
  396. Camouflaged Butterfly
  397. Cantor Set and Function
  398. Cantor's Theorem [Java]
  399. Carnot's Theorem
  400. Carnot's Theorem
  401. Carnot's Theorem from Ptolemy's Theorem
  402. Carnot's Theorem (Generalization of Wallace's theorem) [Java]
  403. Carnot's Theorem for Conics
  404. Carpet With a Hole [Java]
  405. Carpets Theorem [Java]
  406. Casey's Theorem [Java]
  407. Cassini's Ovals and Geometric Optimization [JavaScript, GeoGebra]
  408. centers of similitude
  409. Centroid, a Characteristic Property Of
  410. Centroid and Circumcenter in Isosceles Tetrahedra
  411. Centroid and Incenter in Isosceles Tetrahedra
  412. Centroid on the Incircle in Isosceles Triangle
  413. Centroid on the Incircle in Right Triangle
  414. Centroids and Circumcenters
  415. Centroids in a Polygon [Java]
  416. Cevian Parallelogram [JavScript, GeoGebra]
  417. Chasing Angles Among Angle Bisectors [JavaScript]
  418. Chasing Angles in Pascal's Hexagon [Java]
  419. Circle, Isosceles Triangle and Fixed Point [Java]
  420. Circle Center by Paperfolding
  421. Circle Centers on Radical Axes [Java]
  422. Circle Chains on Napoleon Triangles [Java]
  423. Circle Concurrence on Circumcircle/a> [JavaScript, GeoGebra]
  424. Circle in a Square Inscribed in a Circle [Java]
  425. Circle Rotations and Fixed Points
  426. Circles in Barycentric Coordinates
  427. Circles on the sides of a triangle from the 2005 Austrian MO
  428. Circles Tangent to Circumcircle [Java]
  429. Circles Tangent to Medians at the Centroid [JavaScript, GeoGebra]
  430. Circles with Tangent Diameters [Java]
  431. Ceva and Menelaus Meet on the Roads
  432. Ceva in Circumscribed Quadrilateral
  433. Ceva's Theorem
  434. Ceva's Theorem and Fibonacci Bamboozlement [Java]
  435. Cevian Cradle [Java]
  436. Cevian Cradle II [JavaScript, GeoGebra]
  437. Cevian Nest [Java]
  438. Cevian Triangle [Java]
  439. Cevians And Semicircles [JavaScript]
  440. Cevians Through the Circumcenter
  441. Chain of Inscribed Circles [Java]
  442. Chaos, Emergence of [Java]
  443. Characteristic Property Of Right Triangles
  444. Chasles' Theorem
  445. Cherchez le quadrilatère cyclique [Java]
  446. Cherchez le quadrilatère cyclique II [Java]
  447. Chords, Concurrency and Orthic Triangle [Java]
  448. Chromatic Number of the Plane
  449. Chvatal's Art Gallery Theorem [Java]
  450. Circle and Hyperbola as Lighthouse Curves
  451. Circle and Hyperbola as Lighthouse Curves II
  452. Circle Crosses Triangle [Java]
  453. Circle Concurrency and Spiral Similarity [Java]
  454. Circle Division by Euclid and Leonardo [Java]
  455. Circle of Apollonius in Equilateral Triangle
  456. Circle of Similitude [Java]
  457. Circle Rotations and Fixed Points [JavaScript, GeoGebra]
  458. Circle through the Circumcenter [Java]
  459. Circle through the Incenter [Java]
  460. Circle through the Incenter And Antiparallels [Java]
  461. Circle-Stacking Theorem [Java]
  462. Circles And Parallels [Java]
  463. Circles and Semicircles in Rectangle [Java]
  464. Circles Cover a Quadrilateral [Java]
  465. Circles in a Circular Segment
  466. Circles in a Regular Polygon [Java]
  467. Circles in Morley's Triangles [Java]
  468. Circles Lined on the Legs of a Right Triangle [Java]
  469. Circles On Cevians [Java]
  470. Circles through the Orthocenter [Java]
  471. Circles with Equal Collinear Chords [Java]
  472. Circular Poggendorff Illusion [Java]
  473. Circle Inscribed in a Circular Segment [Java]
  474. Circumcenter and Orthocenter
  475. Circumcenter and Orthocenter Are Isogonal Conjugate
  476. Circumcenter on Angle Bisector [Java]
  477. Circumcevian Triangle [Java]
  478. Classification of Quadrilaterals [Java]
  479. Cleavance Center [Java]
  480. Cleaver [Java]
  481. Clifford Algebras
  482. Clifford's Chain [Java]
  483. Climbing Pyramidal Slopes
  484. Clough's theorem: the simplest proof [JavaScript, GeoGebra]
  485. Coaxal Circles on Perpendicular Bisector [Java]
  486. Coaxal Circles Theorem [Java]
  487. Collage Theorem [Java]
  488. Collinear Intersections and Products of Ratios [JavaScript, GeoGebra]
  489. Collinearity from the IMO 2013 (Problem 4) [Javacript, GeoGebra]
  490. Collinearity in Bicentric Quadrilaterals [Java]
  491. Collinearity in Tangent Circles
  492. Collinearity via Concyclicity [Java]
  493. Collinearity with the Orthocenter [Java]
  494. Color Cycling on the Mandelbrot Set [Java]
  495. Coloring Plane with Three Colors
  496. Coloring Points in the Plane
  497. Common Centroids Lead to Equilateral Triangle [JavaScript, GeoGebra]
  498. Common Chord and a Tangent [Java]
  499. Common Tangents to Two Circles I [Java]
  500. Common Tangents to Two Circles II [Java]
  501. Compass Only Construction - A Chord Tangent to an Inner circle [Java, GeoGebra]
  502. Complete Quadrilateral [Java]
  503. Complex Numbers and Geometry
  504. >Concurrence in Right Triangle
  505. Concurrence on a Circle [JavaScript, GeoGebra]
  506. Concurrence Not from School Geometry [Java, GeoGebra]
  507. Concurrency of Medians and Medial Triangles
  508. Concurrency of the Altitudes in a Triangle - Trigonometric Proof
  509. Concyclic Points at the IMO 2014 [JavaScript, GeoGebra[
  510. Concyclicity in Rectangle [Java]
  511. Concurrence in Equilateral Triangle [JavaScript,GeoGebra]
  512. Concurrence of Ten Nine-Point Circles [JavScript, GeoGebra]
  513. Concurrency in the Intouch Triangle [Java]
  514. Concurrent and Parallel Lines in Parallelogram [JavaScript, GeoGebra]
  515. Concurrent Cevians and a Conic through Their Feet [JavaScript, GeoGebra]
  516. Concyclic Points from Midpoint of an Arc [GeoGebra, JavaScript]
  517. Concyclic Incenters in Bicentric Quadrilateral [JavaScript, GeoGebra]
  518. Concyclic Points in Inscriptible Quadrilateral [JavaScript, GeoGebra]
  519. Concyclicity from Collinearity [JavaScript,GeoGebra]
  520. Concyclicity in Two Semicircles [JavaScript, GeoGebra]
  521. Concyclic Points of Two Ellipses with Orthogonal Axes [JavaScript, GeoGebra]
  522. Condition to Have a 60 Degrees Angle
  523. Concyclic Circumcenters: A Dynamic View [Java]
  524. Concyclic Points in a Triangle
  525. Concyclic Points in Bride's Chair [Java]
  526. Concyclic Points in Equilateral Bumps [Java]
  527. Conic from Parallel Chords [JavaScript, GeoGebra]
  528. Conic in Hexagon [Javascript, GeoGebra]
  529. Conic in Mixtilinear Incircles [JavaScript, GeoGebra]
  530. Conic Sections
  531. Conic Sections as Loci of Points [Java]
  532. Conics Intersecting Sides Of A Triangle [JavaScript, GeoGebra]
  533. Conics in Triangle [JavaScript, GeoGebra]
  534. Conics Related To In- and Excircles [JavaScript, GeoGebra]
  535. Conjugate Diameters in Ellipse [Java]
  536. Consecutive Isosceles Decomposition [Java]
  537. Constant Chord
  538. Constrained Area in Triangle
  539. Constant Ratio on Circle [JavaScript, GeoGebra]
  540. Construct Triangle from Angle, Inradius, and Altitude [JavaScript, GeoGebra]
  541. Construct Triangle by Angle, Median, and Circumradius [JavaScript, GeoGebra]
  542. Construct Triangle by Angle Bisector, Altitude, and Side [JavaScript, GeoGebra]
  543. Construct Triangle by Angle, Altitude and Median [JavaScript, GeoGebra]
  544. Construct Triangle from Altitude, Median and Inradius [JavaScript, GeoGebra]
  545. Constructing a triangle from its angle bisectors is in general impossible
  546. Construction: Parallel Line through Point
  547. Construction and Properties of Mixtilinear Incircles [JavaScript, GeoGebra]
  548. Construction and Properties of Mixtilinear Incircles 2 [JavaScript, GeoGebra]
  549. Construction of a Cyclic Quadrilateral
  550. Construction of a Square from the 2008 Austrian MO
  551. Construction of a Triangle from an Angle, Circumcenter and Incenter
  552. Construction of a Triangle from the Circumcenter, Orthocenter and Incenter
  553. Construction of a Triangle from the Circumradius, Inradius, and an Altitude
  554. Construction of a Triangle from a Side, the Median and the Angle Bisector
  555. Construction of a Triangle from Two Vertices and the Centroid
  556. Construction of an Oval - the Roman Way [Java, GeoGebra]
  557. Construction of Conics from Pascal's Theorem [Java]
  558. Construction of Regular Pentagon by H. W. Richmond
  559. Construction of Thebault Circles [JavaScript, GeoGebra]
  560. Construction of the Angle Bisector [Java]
  561. Construction of the Perpendicular Bisector [Java]
  562. Construction of Triangle from Side, Angle, and that Angle's Bisector
  563. Construction problem [Java]
  564. Constructions Related To An Inaccessible Point
  565. Construction with the Compass Only
  566. Continuous Line Illusion [Java]
  567. Convex Polygon Is the Intersection of Half Planes [Java]
  568. Copernicus' Theorem [Java]
  569. Construction with Optimization in Angle - Problem the 1979 USA Mathematical Olympiad
  570. cos(36°) = (1 +5)/4
  571. cos 75 + cos 45 = cos 15
  572. Cosine Law
  573. Counting Triangles and Segments in a Polygon [Java]
  574. Cross Points in a Polygon [Java]
  575. Cross-Ratio
  576. Crossed-Lines Construction of Shapes of Constant Width [Java]
  577. Crossing Number of a Graph
  578. Cube Counting Ambiguity [Java]
  579. Cultivating Regular Pentagons
  580. Curious Irrationality in Square
  581. Curry's Paradox [Java]
  582. Cut the Cone [Java]
  583. Cut the Cube [Java]
  584. Cutting a Hole in Half [JavaScript, GeoGebra]
  585. Cut the Cylinder [Java]
  586. Cutting Circle to Rearrange Two Dots [JavaScript]
  587. Cutting Squares
  588. Cutting Triangle in Two by a Line through a Point [Java, GeoGebra]
  589. Cutting Triangles off Regular Hexagon
  590. Cyclic Hexagon [Java]
  591. Cyclic Quadrilateral, Angle Bisector And Isosceles Triangle
  592. Cyclic Quadrilateral, Concurrent Circles and Collinear Points [Java]
  593. Cyclic Quadrilateral from the USAMO
  594. Cycloids [Java]
  595. Dan Sitaru's Inequality with Tangents II
  596. Dancing Rectangles Model Auxetic Behavior [Java]
  597. Dancing Squares or a Hinged Plane Tessellation [Java]
  598. Dao's Archimedean Twins [JavaScript, GeoGebra]
  599. Dao's Archimedean Twins - Second Pair [JavaScript]
  600. Dao's Archimedean Twins - Third Pair [JavaScript]
  601. Dao Thanh Oai's Invariant
  602. Dao's Variant of Thébault's First Problem [JavaScript, GeoGebra]
  603. David Richeson's Extention of an Old Japanses Theorem [Java]
  604. Day's Sine Illusion [Java]
  605. Decompose Cyclic Quadrilaterals into k≥4 Cyclic Quadrilaterals
  606. A Decomposition of Isosceles Triangles into 4 Isosecles Triangles
  607. Delboeuf Illusion [Java]
  608. Delian Problem Solved [Java]
  609. Desargues' Hexagon [Java, GeoGebra]
  610. Desargues in the Bride's Chair (with Pythagoras)
  611. Desargues' Theorem [Java]
  612. Determination ofπ
  613. Diagonal Count [Java]
  614. Diagonals in a Cyclic Quadrilateralli>Diagonals in a Polygon Parallel to Sides <
  615. Diameters and Chords [Java]
  616. Dimensionless Inequality in the Euclidean Plane
  617. Directly Similar Figures [Java]
  618. Disappearing Lines puzzle [Java]
  619. Discovery of Duane DeTemple [Java]
  620. Dissection of a 10×13 Rectangle into Two Chessboards
  621. Dissection of a Vase [Java]
  622. Dissection of Cyclic Quadrilateral [Java]
  623. Dissection of Triangle into Rhombus [Java]
  624. Dissection of Triangle into Rhombus by Hubert Shutrick [Java]
  625. Distance
  626. Distance Between Projections
  627. Distance between the Orthocenter and Circumcenter
  628. Distance Formula
  629. Distorted Lines Illusion [Java]
  630. Divergent Spirals Illusion [Java]
  631. Divide a Circle into N Parts of Equal Area
  632. Divide a segment into n equal parts
  633. Divide Triangle by Lines Parallel to Base [JavaScript, GeoGebra]
  634. Dividing Evenly a Quadrilateral [Java]
  635. Dividing Evenly a Quadrilateral II [Java]
  636. Dorin Marghidanu's Inequality with Maximum Side
  637. Double Generation Theorem [Java]
  638. Drawing circles [Java]
  639. Droz-Farny Circles [Java]
  640. Droz-Farny Line Theorem [Java]
  641. Droz-Farny Theorem - an Analytic Solution [JavaScript, GeoGebra]
  642. Dual of Maxwell's Theorem
  643. Duplication of the Cube
  644. Dynamic Construction of Ellipse and Other Curves [Java]
  645. Dynamic Software as Serendipity Enhancement [Java, GeoGebra]
  646. A. G. Samosvat's Proof by Dissection of the Pythagorean Theorem (#104) [GeoGebra]
  647. E. W. Dijkstra's Proof of the Pythagorean Theorem [Java]
  648. Early Refinement of the Ionescu-Weitzenbock Inequality
  649. Easy Construction of Bicentric Quadrilateral [Java]
  650. Easy Construction of Bicentric Quadrilateral II [Java]
  651. Egyptian Triangle By Paper Folding
  652. Egyptian Triangle By Paper Folding II
  653. Egyptian Triangle By Paper Folding III
  654. Eight Equal Tangents [Java]
  655. Eight Point Circle [Java]
  656. Elementary Introduction into the Concept of Area
  657. Ellipse Between Two Circles [Java]
  658. Ellipse in Arbelos [Java]
  659. Ellipse Touching Sides of Triangle at Midpoints [Java, GeoGebra]
  660. Emil Stoyanov's From Reflections to Altitudes
  661. Emil Stoyanov's New Year's Problem
  662. Emil Stoyanov's New Year's Problem, a Sequel
  663. Equal And Perpendicular Segments in a Square
  664. Equal Angles in Two Circles [Java]
  665. Equal Angles in Two Circles II [Java]
  666. Equal areas In Circle [JavaScript]
  667. Equal Areas in Equilateral Triangle [Java]
  668. Equal Areas In Parallelogram à la Pythagoras [Java]
  669. Equal Areas in Regular 2n-gons [Java]
  670. Equal Chords in Crossing Circles [Java]
  671. Equal Circles, Medial Triangle and Orthocenter [Java]
  672. Equal Incircles Theorem [Java]
  673. Equiangular p-gons
  674. Equichordal points: Just Do It [Java]
  675. Equidecomposition of a Rectangle and a Square [Java]
  676. Equidecomposition of Two Rectangles [Java]
  677. Equidecomposition of a Triangle and a Rectangle [Java]
  678. Equidecomposition of a Triangle and a Rectangle II [Java]
  679. Equidecomposition of Two Parallelograms [Java]
  680. Equilateral and 3-4-5 Triangles [Java]
  681. Equilateral triangle and squares
  682. Equilateral Triangle from Equilateral Triangle
  683. Equilateral Triangle in Equilateral Triangle [JavaScript, GeoGebra]
  684. Equilateral Triangle on a Closed Curve [JavaScript, GeoGebra]
  685. Equilateral Triangle on Angle Bisectors
  686. Equilateral Triangle on Parallel Lines [Java]
  687. Equilateral Triangle on Parallel Lines II
  688. Equilateral Triangle on Three Lines [JavaScript, GeoGebra]
  689. Equilateral Triangle in Square and Its Circumcircle
  690. Equilateral Triangle in Square with the Cevians through Its Apex
  691. Equilateral Triangle in Square And the Pedal Circle of Its Apex
  692. Equilateral Triangle, Straight Line and Tangent Circles [Java]
  693. Equilateral Triangles and Incircles in a Square
  694. Equilateral Triangles formed by Circumcenters [JavaScript, GeoGebra]
  695. Equilateral Triangles on Diagonals of Antiequilic Quadrilateral [Java]
  696. Equilateral Triangles On Sides of a Parallelogram [Java]
  697. Equilateral Triangles On Sides of a Parallelogram II [Java]
  698. Equilateral Triangles on Sides of a Parallelogram III [JavaScript, GeoGebra]
  699. Equilateral Triangles on Sides of a Quadrilateral [Java]
  700. Equilic Quadrilateral I, a Flawed Proof [Java]
  701. Equilic Quadrilateral I, A Variation [Java]
  702. Equilic Quadrilateral II [Java]
  703. Erdös-Mordell Inequality
  704. Escher's Theorem [Java]
  705. Euclid's Fifth Postulate
  706. Euclid'sElements Reference Page
  707. Euclid I.43 [Java]
  708. Euclid I.43 Extended [Java]
  709. Euclidean Construction of Center of Ellipse [Java]
  710. Euclidean Construction of Tangent to Ellipse
  711. Euler Inequality in Triangle
  712. Euler Line Cuts Off Equilateral Triangle [Java]
  713. Euler Line and 9-Point Circle [Java]
  714. Euler Line Through a Vertex
  715. Euler's Formula and Poncelet Porism
  716. Euler Line in a Triangle with a 60 Degrees Angle
  717. Every Parallelogram Is a Rectangle
  718. Excircle in Equilateral Triangle
  719. Excircles in Trapezoid
  720. Exeter Point [Java, GeoGebra]
  721. Existence of the Circumcenter [Java]
  722. Existence of the Orthocenter [GeoGebra]
  723. Existence of the Euler Line: An Elementary Proof [Java]
  724. Existence of the Incenter: a Second Look
  725. Experimentation with Dynamic Geometry Software: An Example [Java]
  726. Exploring Vecten's Wreaths with Linear Algebra
  727. Expressions Invariant under Projecive Mappings
  728. Exterior Angle Theorem - an appreciation
  729. External Angle Bisector [Java]
  730. Extouch Triangle in Poncelet Porism [Java]
  731. Extra Feature of Van Aubel Configuration [JavaScript,GeoGebra]
  732. Extras in Bottema's Configuration [JavaScritpt, GeoGebra]
  733. Extremal Problem in a Quadrilateral
  734. Extremal Distance Ratio [GeoGebra]
  735. Extremal Problem in a Circular Segment
  736. The Extreme Principle
  737. Eye-to-Eye Theorem I [JavaScript, GeoGebra]
  738. Eye-to-Eye Theorem II [JavaScript, GeoGebra]
  739. Eyeball Theorem [JavaScript, GeoGebra]
  740. Eyeball Theorem Rectified [JavaScript]
  741. Eyeballing a Ball [JavaScript, GeoGebra]
  742. Eyeballs Projected [JavaScript, GeoGebra]
  743. Fagnano's problem [Java]
  744. Faulty Symmetry
  745. Fermat's Hexagon [JavaScript, GeoGebra]
  746. Fermat in a Triangle with a 60 Degrees Angle
  747. Fermat point and 9-point Centers [Java]
  748. Fermat Point Several Times Over
  749. Feuerbach's Theorem: A Proof [Java]
  750. Find a Common Chord of Given Length [Java]
  751. Find the Angle! [Java]
  752. Finding a Parallelogram in 3D
  753. Finding Circle Center By Ruler Alone [Java]
  754. Finding the Circumradius of the Excentral Triangle
  755. Five Concyclic Points [Java]
  756. Five Incircles in a Square [Java]
  757. Five Incircles Theorem [Java]
  758. Five Squares in Complex Numbers [Java, GeoGebra]
  759. Fixed Point in a Kite - Problem from the 1993 Asian Pacific MO
  760. Fixed Point in Isosceles and Equilateral Triangles
  761. Fixed Point on Perpendicular Bisector [GeoGebra, JavaScript]
  762. Fixed Point of Circles Orthogonal to the Given One [Java]
  763. Fixed points from 2007 Irish Mathematical Olympiad
  764. Fleury's Algorithm and Euler's Paths and Cycles [Java]
  765. FJG Capitan's Sangaku
  766. Focal Definition of Ellipse [Java]
  767. Focal Definition of Parabola [Java, GeoGebra]
  768. Focus and Directrix of Ellipse [Java]
  769. Focus on the Eyeball Theorem [JavaScript, GeoGebra]
  770. Folding Square in a Line through the Center [Java, GeoGebra]
  771. Fold Square into Equilateral Triangle [JavaScript]
  772. Following the Hilbert Curve [Java]
  773. Foot of Altitude and Minimum Distance [Java]
  774. For Equality Choose Angle Bisector [JavaScript, GeoGebra]
  775. For every object there is a distance at which it looks its best.
  776. Ford's touching circles
  777. Four Centroids and Parallels [Java]
  778. Four Circles and a Line [GeoGebra]
  779. Four Circles In a Triangle [Java]
  780. Four Concurrent Lines in a Cyclic Quadrilateral [Java]
  781. Four Construction Problems [Java]
  782. Four Crossing Circles [Java]
  783. Four Geometric Problems of Antiquity
  784. Four Golden Circles
  785. Four Hinged Squares [Java]
  786. Four Incident Circles [Java]
  787. Four Incircles in Equilateral Triangle [Java]
  788. Four Isosceles Triangles Hinged at Vertices [JavaScript, GeoGebra]
  789. Four 9-Point Circles in a Quadrilateral [Java]
  790. Four Pedal Circles [Java]
  791. Four Touching Circles [Java]
  792. Four Touching Circles II [Java]
  793. Four Touching Circles III [Java]
  794. The Four Touching Circles Problem IV [Java, GeoGebra]
  795. Four Triangles, One Circle [Java]
  796. Four Turtles (or Bugs, or Dogs, etc.) [Java]
  797. Fractal curves and dimension [Java]
  798. François Viète's Reduction of CCC to PCC [Java, GeoGebra]
  799. Friendly Kiepert's Perspectors [Java]
  800. From 3 to Golden Ratio in Semicircle
  801. From Angle Bisector to 120°120 degrees Angle
  802. From Arbitrary Hexagon to Regular One [JavaScript, GeoGebra]
  803. From Arbitrary Pentagon to Regular One [JavaScript, GeoGebra]
  804. From Equilateral Triangle and Square to Golden Ratio
  805. From Foci to a Tangent in Ellipse [Java]
  806. From One Collinearity to Another
  807. From Perpendicular Center Lines to Concyclic Points
  808. From Straight Line to Regular Hexagon [JavaScript, GeoGebra]
  809. From Triangle Inequality to Inequality in Triangle
  810. Fun Identity in Right Triangle
  811. Functions And Triangles
  812. Fundamental Theorem of 3-Bar Motion [Java]
  813. Further Arithmetic Progression in 30-60-90 Triangle
  814. Further Properties of Peculiar Circles
  815. Further properties of Van Aubel Configuration [JavaScript, GeoGebra]
  816. Fuss' Theorem [Java]
  817. Garcia's Archimedean Quadruplets [JavaScript, GeoGebra]
  818. Garcia's Two Circles Lemmas [JavaScript, GeoGebra]
  819. Garcia-Feuerbach Collinearity [JvaScript, GeoGebra]
  820. Garfield's Ghost Revisited - by Tony Foster
  821. Generalizing a Romanian Olympiad Problem [Java]
  822. Geometric/Trigonometric Observation/Exercise
  823. Geometric Illustration of a Convergent Series
  824. Geometric Mean In Trapezoid
  825. Geometric Mean Sangaku
  826. Geometric Meaning of the Geometric Mean
  827. Geometric Optimization from the Asian Pacific Mathematical Olympiad [Java]
  828. Geometric Proof of Hlawka's Inequality
  829. Geometric Proofs Of the Irrationality of Square Roots
  830. Geometry, Algebra, and Illustrations
  831. Gergonne and Medial Triangles Are Orthologic [Java]
  832. Gergonne and Soddy Lines Are Perpendicular [Java]
  833. Gergonne in Ellipse [Java]
  834. Gergonne and Van Obel Theorems
  835. Getting the first digits of Pi by counting collisions
  836. Gion Shrine Problem
  837. Given Parabola, Find Axis
  838. Glide Reflection [Java]
  839. Golden Ratio in Geometry
  840. Golomb's inductive proof of a tromino theorem [Java]
  841. Gothic Arc [Java]
  842. Graph Theory [Java]
  843. Grebe: from Ladies' Diary to Carroll's Pillow [Java]
  844. Grebe's Theorem
  845. Greg Markowsky's Problem for Parabola [Java]
  846. Gregoie Nicollier's Proof of Napoleon's Theorem
  847. Griffiths Points in Cyclic Quadrilateral [Java]
  848. Griffiths' Theorem
  849. Half Turn, Reflection in Point [Java]
  850. Halving a square
  851. Harmonic Mean in Geometry
  852. Harmonic Mean Sangaku [Java]
  853. Harmonic Ratio
  854. Harmonic Ratio in Complex Domain
  855. Hart Circle [Java]
  856. Hart's Inversor [Java]
  857. Haruki's Lemma [Java]
  858. Haruki's Theorem
  859. Hausdorff Distance
  860. Hearty Munching on Cardioids [Java]
  861. Height/Width Interplay Illusion [Java]
  862. Helly's Theorem
  863. Hering Illusion [Java]
  864. Hermann Grid Illusion [Java]
  865. Heron's formula
  866. Heron's Formula: a Proof [Java]
  867. Heron's Problem [Java]
  868. Heron in Trapezoid [JavaScript, GeoGebra]
  869. Hexagon Parallel to Medial Triangle [Java]
  870. Hexagon Parallel to Orthic Triangle [Java]
  871. Hexagons in a Square
  872. Hidden Orthogonality [JavaScript, GeoGebra]
  873. Hinged Greek Cross Tessellation [Java]
  874. Hinged Squares [Java]
  875. Hinged Squares II [JavaScript, GeoGebra]
  876. Hippocrates' Squaring of a Lune [Java]
  877. Hippocrates' Squaring of Lunes
  878. Hjelmslev Theorem [Java]
  879. Hlawka in Convex Quadrilateral
  880. Homologous Lines under Three Spiral Similarities [Java]
  881. Homothety [Java]
  882. Homothety between In- and Excircles [Java]
  883. Homothety in Equilateral Triangles [JavaScript, GeoGebra]
  884. Homothety in Three Tangent Circles
  885. Homothety in Three Tangent Circles II
  886. Hooper's Paradox [Java]
  887. How Do Angle Trisectors Divide the Area?
  888. How Fast Does One's Shadow Grow?
  889. How Long Are the Angle Bisectors of a Degenerate Triangle?
  890. How to Construct a Radical Axis [Java, GeoGebra]
  891. How to Construct Tangents from a Point to a Circle [Java, GeoGebra]
  892. Hung Nguyen Viet's Inequality with Radicals and Chebyshev
  893. Hunting Right Angles [Java]
  894. Huygens' Problem
  895. Ian McGee's Observation [Java]
  896. IMO 1998 Problem 1
  897. IMO 2004, Problem 5
  898. IMO 2006, Problem 1
  899. Impossible Fork [Java]
  900. Impossible Frame [Java]
  901. Impossiblity Condition in Concurrent Cevians
  902. Importance of Having an Angle of 60 Degrees
  903. Importance of Occluders: Motion Binding [Java]
  904. In the Spirit of Thebault I [Java, GeoGebra]
  905. In the Wasan Spirit
  906. Incenters in Cyclic Quadrilateral [Java]
  907. Incidence in Feuerbach's Theorem [Java]
  908. Incircle in Equilateral Triangle
  909. Inequalities in Triangle
  910. Inequality in Quadrilateral
  911. Inequality in Rectangle
  912. An Inequality with a Variety of Circumradii
  913. Inequality with Cubes and Cube Roots
  914. An Inequality with Inradius and Excenters
  915. Inequality with Roots, Squares and the Area
  916. An Inequality with Two Sets of Cevians
  917. Infinitude of Primes - A Topological Proof
  918. Inradii Relation in Right Triangle
  919. Inscribed and Central Angles in a Circle [Java]
  920. Inscribed Angles [Java]
  921. Inscriptible and Exscriptible Quadrilaterals [Java]
  922. Inscriptible Quadrilateral: An Illustration [Java]
  923. Inscriptible Quadrilateral of Triangle Incenters [JavaScript, GeoGebra]
  924. Integer Chord in a Polynomial Graph
  925. Integer Triangles with Two Angles in the Ratio 1 : 2 [JavaScript, GeoGebra]
  926. Internal Tangents to Three Circles [Java]
  927. Interpretation of the coordinate formula for the dot product in 3D
  928. Intersecting Chords Theorem
  929. Intersections of a Circle with the Four Quadrants [Java]
  930. Intouch Triangle in Poncelet Porism [Java]
  931. Invariance in Orthodiagonal Quadrilaterals [Java]
  932. Invariant Area Sweep Implies Pythagorean Theorem [Java]
  933. Inverse Similarity through Reflections
  934. Inversion: Reflection in a Circle [Java]
  935. Involution on the Projective Line
  936. Is Every Trapezoid Parallelogram? [Java]
  937. Is X a Midpoint of a Chord [JavaScript, GeoGebra]
  938. Isosceles Tetrahedra Characterization via Inequalities
  939. Isogonal Concurrencies [JavaScript, GeoGebra]
  940. Isogonal Lemma [JavaSCript, GeoGebra]
  941. Isosceles Configuration in Triangle [JavaScript, GeoGebra]
  942. Isosceles Tetrahedron
  943. Isosceles Trapezoid In Cyclic Quadrilateral [JavaScript, GeoGebra]
  944. Isosceles Triangle with Two Points on Base
  945. Isogonal and Isotomic Conjugalities [Java]
  946. Isogonal Concurrency [Java]
  947. Isogonal image of the circumcircle [Java]
  948. Isoperimetric Theorem and Inequality
  949. Isosceles on the Sides of a Triangle [Java]
  950. Isotomic Reciprocity [JavaScript, GeoGebra]
  951. Isotomy and Isogonality Hand-in-Hand [Java]
  952. Iterations and the Mandelbrot Set [Java]
  953. Iterations on a Circle Through Three Points [Java]
  954. Iterations on Euler Lines [Java]
  955. Igor Sharygin's Problem in Circumscribed Quadrilateral
  956. J. Casey's Additions to Euclid I.47
  957. Jan Stevens' proof of E. W. Dijkstra's Generalization of the Pythagorean theorem
  958. Joachimsthal's Notations
  959. John Sharp's Paradox [Java]
  960. Johnson Circles [Java]
  961. Join Circles by Given Segment [Java]
  962. Joined Common Chords of Napoleon's Circumcircles [JavaScript, GeoGebra]
  963. Jordan and Kober Inequalities, PWW
  964. Jordan Curve Theorem
  965. Joseph Keech in Bride's Chair [Java]
  966. Judd Illusion [Java]
  967. Julia sets indexing [Java]
  968. K. Knop's Problem with Two Regular Pentagons And an Equilateral Triangle
  969. Kanizsa Triangle [Java]
  970. Kiepert's Centroid [JavaScript, GeoGebra]
  971. Kiepert's Theorem [Java]
  972. Kiepert's Triangles Graduate to Ears of Arbitrary Shape [JavaScript, GeoGebra]
  973. Klamkin's Quickie via Peru Geometrico
  974. Knots [avi movie]
  975. Knots on a Torus [Java]
  976. Kürschak's Tile and Theorem [Java]
  977. La Hire's Theorem [Java]
  978. Langman's Paradox [Java]
  979. LCC: Apollonius' Problem with Two Circles and a Line [Java, GeoGebra]
  980. Lean Napoleon's Triangles [Java]
  981. Length of a Median
  982. Length of the diagonal of the unit square equals the square root of 2
  983. Lennes' Polyhedron [Java]
  984. Leo's Lemma, Second Application
  985. Leo Giugiuc's Inequality for the Medians
  986. Leo Giugiuc's Inequality in Triangle, Solely with Cotangents
  987. Leo Giugiuc's Proof of Napoleon's Theorem
  988. Leo Giugiuc's Trigonometric Lemma
  989. Leo Giugiuc's Second Lemma And Applications
  990. Leonardo's Petals
  991. Lepidoptera of the Circles [Java]
  992. Leuenberger's Inequality for Medians, Inradius and Circumradius
  993. Lighthouse at Fermat Points [JavaScript, GeoGebra]
  994. Line IO in Bicentric Quadrilaterals
  995. Line Not Through a Center of Similarity [JavaScript, GeoGebra]
  996. Line Through a Center of Similarity [JavaScript, GeoGebra]
  997. Line through a Point in an Angle
  998. Line, Circle, and Fixed Points [Java]
  999. Linear Function with Coefficients in Arithmetic Progression [Java, GeoGebra]
  1000. Lines Crossing Circles at Vertices of Equilateral Triangle
  1001. Lines through Circles at Vertices of Equilateral Triangle [JavaScript]
  1002. LLC: Apollonius' Problem with Two Lines and a Circle [Java, GeoGebra]
  1003. Lipogrammatic Proof of the Pythagorean Theorem
  1004. Loci of points in a cube
  1005. Locus of Points in a Given Ratio to Two Points [Java]
  1006. Longest segment
  1007. Longitude, Latitude and Distance to the Equator
  1008. Looking Back at Bottema [JavaScript, GeoGebra]
  1009. Luca Moroni's Problem In Equilateral Triangle
  1010. Mach's Conservation of Area and the Pythagorean Theorem
  1011. MacLaurin's Construction of Conics [Java]
  1012. Maimed Cake [Java]
  1013. Malfatti's Problem [Java]
  1014. Malfatti's Problem, Hart's Solution [Java]
  1015. Marian Cucoanes' Inequality With Roots and Powers
  1016. Marian Dinca's Inequality
  1017. Mascheroni Construction of a Regular Pentagon
  1018. Mathematical Droodles [Java]
  1019. Mathematics in Pizzeria [Java]
  1020. MathPro Logo [Java]
  1021. Maximal Properties of the Pythagorean Relation
  1022. Maximum Area Property of Equilateral Triangles
  1023. Maximum Area Property of the Medial Triangle
  1024. Maximum Perimeter Property of the Incircle [Java]
  1025. Maximum Ratio of Similarity - Belarus Olympiad Problem
  1026. Maxwell's Theorem [Java]
  1027. May the Product of Planes Be a Sphere?
  1028. McDougall's Generalization of Ptolemy's Theorem
  1029. Mechanical Proofs of the Pythagorean Theorem
  1030. Median in Touching Circles [Java]
  1031. Medians
  1032. Medians in a Quadrilateral [Java]
  1033. Medians in a Triangle Meet at the Center: a Second Look
  1034. Meisters' Two Ears Theorem
  1035. Menelaus Theorem [Java]
  1036. Metric Relations in a Triangle
  1037. Mickey Might Be a Red Herring in the Mickey Mouse Theorem
  1038. Midline in Quadrilateral [Java, GeoGebra]
  1039. Midline in Similar Triangles [Java]
  1040. Midline in Trapezoid [Java, GeoGebra]
  1041. Midline in Triangle [Java, GeoGebra]
  1042. Midpoint Reciprocity in Napoleon's Configuration [JavaScript,GeoGebra]
  1043. Midpoints and Orthogonality in Isosceles Triangles [Java]
  1044. Midpoints from Gergonne Triangle [Java]
  1045. Midpoints of the Lines Joining In- and Excenters [Java]
  1046. Miguel's Area of Square [JavaScript, GeoGebra]
  1047. Miguel's Tangents: Modern Day Sangaku [JavaScript, GeoGebra]
  1048. Miguel Ochoa's Chords And Tangents [JavScript, GeoGebra]
  1049. Miguel Ochoa's van Schooten Is a Slanted Viviani [JavScript, GeoGebra]
  1050. Miguel Ochoa's van Schooten Like Theorem [JavaScript, GeoGebra]
  1051. Miguel Ochoa's van Schooten Like Theorem II [JavaScript, GeoGebra]
  1052. Miguel Ochoa's van Schooten Like Theorem III [JavaScript, GeoGebra]
  1053. Miguel's Special Trapezoid
  1054. Mikhalev's Octahedrons
  1055. Minesweeper Theorem
  1056. Miquel's Point [Java]
  1057. Miquel's Point of a 4-line Via Spiral Similarity [Java]
  1058. Miquel's Theorem for Circles [Java]
  1059. Miquel Circumcenters [JavaScrirpt, GeoGebra]
  1060. Mirror on the Wall [Java]
  1061. Mirror property of the altitudes [Java]
  1062. Mirror Property of Altitudes via Pascal's Hexagram [Java]
  1063. Mixing Incenter And Orthocenter in Greece
  1064. Mixtilinear Circles and Concurrence [Java]
  1065. Modern Day Sangaku
  1066. Moebius Strip [avi movie]
  1067. Möbius' Strip [Java]
  1068. Models and Metamathematics
  1069. Moment of Inertia of a Regular Polygon [JavaScript]
  1070. Moments in a Peculiar Cyclic Polygon
  1071. Monge via Desargues [Java]
  1072. Monge via Desargues II [Java]
  1073. More of More of Gloden Ratio in Equilateral Triangles
  1074. Morley Constellation [Java]
  1075. Morley's Miracle [Java]
  1076. Morphing [Java]
  1077. Müller-Lyer Illusion [Java]
  1078. Multifaceted Cork [Java]
  1079. Multiplication of Points on a Circle [JavaScript,GeoGebra]
  1080. Multiplication of Points on an Ellipse [JavaScript, GeoGebra]
  1081. Munching on Circles
  1082. Munching on Inscribed Angles
  1083. My logo
  1084. Nagel Line [Java]
  1085. Nagel point [Java]
  1086. Nagel Point and Centroid on Adjacent Isosceles Triangles
  1087. Nagel Point of the Medial Triangle [Java]
  1088. Nagel Point on the Incircle in Isosceles Triangle
  1089. Nagel's Theorem [Java]
  1090. Napoleon's Hexagon [JavaScript, GeoGebra]
  1091. Napoleon's Theorem
  1092. Necker Cube [Java]
  1093. Neuberg Cubic [Java, GeoGebra]
  1094. Neuberg Sangaku [Java]
  1095. Newly Born Pair of Siblings to Archimedes' Twins [Java]
  1096. Newton's Construction of Conics [Java]
  1097. Newton's Theorem [Java]
  1098. Nine Point Center in Square
  1099. Nine Point Circle [Java]
  1100. Nine Point Circle: an Elementary Proof [Java]
  1101. No Equilateral Triangles, Please [Java]
  1102. Nobbs' Points, Gergonne Line [Java]
  1103. Non-Eclidean Geometries
  1104. No-Pedal Collinearity [Java]
  1105. Not So Hidden Homotheties [JavaScript, GeoGebra]
  1106. Novel Concurrency of Perpendicular Bisectors [JavaScript, GeoGebra]
  1107. Number of Regions N Lines Divide Plane
  1108. Occluded Wheel Illusion [Java]
  1109. Olof Hanner's Jigsaw Puzzle [Java]
  1110. On the Difference of Areas
  1111. One More Property of Equilateral Triangles
  1112. One More Seven Circles Theorem [JavaScript, GeoGebra]
  1113. One Sheet Hyperboloid [Java]
  1114. A One-Sided Inequality in Triangle
  1115. One Triangle from Another
  1116. One Triangle from Another II
  1117. Optimal Quadrilateral Inscribed in a Square
  1118. Optimization in a Crooked Trapezoid
  1119. Optimization in Parallelepiped
  1120. Optimization Problem in Acute Angle [Java]
  1121. Octagon in Parallelogram: Overlapping Regions [Java]
  1122. Octagon in Parallelogram [Java]
  1123. Optical Property of Ellipse [Java]
  1124. Orbison illusion [Java]
  1125. Orthic Semiperimeter [Java, GeoGebra]
  1126. Orthic Triangle in a Triangle with a 120 degrees angle
  1127. Orthogonal Lines, Midpoints, and Collinearity [Java, GeoGebra]
  1128. Orthogonality in Isogonal Conjugacy [JavaScript, GeoGebra]
  1129. Orthocenter and Three Equal Circles [Java]
  1130. Orthocenters
  1131. Orthocenters of Two Triangles Sharing Circumcenter and Base [Java]
  1132. Orthocentric System From Rectangle [Java]
  1133. Orthodiagonal and Cyclic Quadrilaterals [Java]
  1134. Orthogonality in Isosceles Triangles [Java]
  1135. Orthogonality in Two Squares [JavaScript, GeoGebra]
  1136. Orthologic Triangles in a Quadrilateral [Java]
  1137. Orthopole [Java]
  1138. Out of Pentagon Sangaku
  1139. Packing shapes in a plane
  1140. Padoa's Inequality
  1141. Pairs of Areas in Equilateral Triangle
  1142. Pairs of Homologous Lines under Spiral Similarities [Java]
  1143. Pairs of Incircles in a Quadrilateral [Java]
  1144. Pantograph [Java]
  1145. Paper Folding & Cutting Sangaku
  1146. Paper Folding Geometry
  1147. Paper strip activities [avi movies]
  1148. Paper strip activities, two strips
  1149. Pappus' Generalization of Euclid I.47 [Java]
  1150. Pappus' Theorem [Java]
  1151. Parabola [Java]
  1152. Parabola and Abutting Equilateral Triangles
  1153. Parabolas Related to the Orthic Triangle [JavaScript, GeoGebra]
  1154. Parabolic Mirror, Illustration [Java]
  1155. Parabolic Mirror, Theory [Java]
  1156. Parabolic Reciprocity [JavaScript, GeoGebra]
  1157. Parabolic Sieve of Prime Numbers
  1158. Paragon [Java]
  1159. Parahexagon [Java]
  1160. Parallel Chords [Java]
  1161. Parallel Chords II [Java]
  1162. Parallel Chords in Conics [Java, GeoGebra]
  1163. Parallel Chords in Ellipse [Java]
  1164. Parallel Chords in Crossing Circles [Java]
  1165. Parallel Lines in a Cyclic Quadrilateral [Java]
  1166. Parallel Lines in a Quadrilateral II [Java] Parallel Lines in a Quadrilateral
  1167. Parallel Lines in Rhombus
  1168. Parallel Lines in a Triangle [Java, GeoGebra]
  1169. Parallels through the Vertices of Equilateral Triangle
  1170. Parallelogram and Ellipses [Java, GeoGebra]
  1171. Parallelogram and Four Equilateral Triangles [JavaScript, GeoGebra]
  1172. Parallelogram and Similar Triangles [Java]
  1173. Parallelogram Illusion [Java]
  1174. Parallelogram in Four Circles [JavaScript, GeoGebra]
  1175. Parallelogram in Parallelogram And in Projection [JavaScript, GeoGebra]
  1176. Parallelogram in Trapezoid
  1177. Parallelogram Iterations [Java]
  1178. Parallelogram Law [Java]
  1179. Parallelogram Law: A PWW [Java]
  1180. Parallelogram Law: A Tessellation [Java]
  1181. Parallelogram with Side Lines through Fixed Points [JavaScript, GeoGebra]
  1182. Partition of point sets in a plane
  1183. Partitioning 3-Space with Circles
  1184. Partitioning a Circle
  1185. Pascal: Necessary and Sufficient [Java]
  1186. Pascal in a Cyclic Quadrilateral [Java]
  1187. Pascal Lines: Steiner and Kirkman Theorems [Java]
  1188. Pascal Lines: Steiner and Kirkman Theorems II [Java]
  1189. Pascal's theorem [Java]
  1190. Peacock's Tail Sangaku
  1191. Peaucellier Linkage [Java]
  1192. Pedal Collinearities [Java]
  1193. Pedal Parallelogram [JavScript, GeoGebra]
  1194. Pedal Polygons [Java]
  1195. Pedal Property in Equilateral Triangle
  1196. Pedal SimilarityPedal Triangle and Isogonal Conjugacy [Java]
  1197. Pedal Triangles of Inverse Points [JavaScript, GeoGebra]
  1198. Pedoe's Theorem [Java]
  1199. Pencils of Cubics
  1200. Pentagon, construction of
  1201. Pentagon And Decagon, Both Regular
  1202. Pentagon in a Semicircle [Java]
  1203. Pentagon Proportions Sangaku
  1204. Perimeters of Convex Polygons, One within the Other
  1205. Perimeters of Parallelogram And Rhombus [JavaScript, GeoGebra]
  1206. Periodic patterns in sin(N) [Java]
  1207. Perpendicular Bisectors in an Inscriptible Quadrilateral [Java]
  1208. Perpendicular Bisectors in an Inscriptible Quadrilateral II [Java]
  1209. Perpendicular lines in a cyclic quadrilateral from 1975 Canadian Mathematical Olympiad
  1210. Perpendiculars in Parallelogram [JavaScript, GeoGebra]
  1211. Perspective Triangles in Circle
  1212. Pick's Theorem [Java]
  1213. Phantom Circle and Recaptured Symmetry
  1214. Planar Sets with Integer Distances between Points
  1215. Plane Filling Curves [Java]
  1216. Plane Isometries
  1217. Plane Isometries As Complex Functions
  1218. Plato's Geometric Numbers: can you better Sam Loyd?
  1219. Pleasant Proportions in Triangle
  1220. Poggendorff's Illusion
  1221. Point common to two similar rectangles [Java]
  1222. Point in a Square
  1223. Point on Bisector in Right Angle
  1224. Points Generated by the Nine Points
  1225. Points on Incircle: Another Look
  1226. Polar Circle [Java]
  1227. Poles and Polars [Java]
  1228. Polygon in a Rectangle
  1229. Polygons: formality and intuition [Java]
  1230. Polygons Formed by Perpendicular Bisectors [Java]
  1231. Pompeiu's Theorem
  1232. Poncelet's Porism [Java]
  1233. Poncelet's Porism in Ellipses [Java]
  1234. Poncelet's Theorem [Java]
  1235. Ponzo Illusion [Java]
  1236. Ponzo Illusion II [Java]
  1237. Possible or Impossible? [Java]
  1238. Power of a point with respect to a circle
  1239. PCC: Apollonius' Problem with Two Circles and a Point [Java, GeoGebra]
  1240. PLC: Apollonius Problem with a point, a line, and a circle [Java, GeoGebra]
  1241. PLL: Apollonius' Problem with Two Lines and a Point [Java, GeoGebra]
  1242. PPC: Apollonius' Problem with Two Points and a Circle [Java, GeoGebra]
  1243. PPL: An Elementary Solution [Java, GeoGebra]
  1244. PPL: Apollonius' Problem with Two Points and a Line [Java, GeoGebra]
  1245. Prasolov's Pythagorean Identity
  1246. Praying Eyes Theorem [JavaScript, GeoGebra]
  1247. Problem 1 from the 2006 IMO
  1248. Problem 1 from the EGMO2017
  1249. Problem 1 from the Ninth Nordic Mathematical Contest (1994)
  1250. Problem 11984 From the American Mathematical Monthly
  1251. Problem 3 from the EGMO2017
  1252. Problem 4 from the 1959 IMO: Construction of a Right Triangle [Java, GeoGebra]
  1253. Problem 4, 1975 USA Math Olympiad and the Radical Axis [Java]
  1254. Problem 4, 1975 USA Math Olympiad and Isosceles Triangles [Java]
  1255. Problem 4, 1975 USA Math Olympiad: Normals and Tangents [Java]
  1256. Problem 4, 1975 USA Math Olympiad: Problem 4, 1975 USA Math Olympiad: The Final Touch [Java]
  1257. Problem 4 from the 2016 OBJM TST
  1258. Problem 4 from the IMO 2009
  1259. Problem 4 from the 4th BJMO Team Selection Test
  1260. Problem 4087 from Crux Mathematicorum
  1261. Problem 4096 from Crux Mathematicorum
  1262. Problem in an Equilateral Triangle [Java]
  1263. Problem 4 from the IMO 2013 - Synthetic Solution [Javacript, GeoGebra]
  1264. Problem 4160 from the Crux Mathematicorum
  1265. Problem A-2 from the 2002 Putnam Math Competition
  1266. Problem A-6 from the 1992 Putnam Math Competition
  1267. Problem CC156 From Crux Mathematicorum
  1268. Problem in a Special Trapezoid
  1269. Problem in an Equilateral Triangle II [Java]
  1270. Problem in Direct Similarity [JavaScript, GeoGebra]
  1271. Problem in Three Squares [Java]
  1272. Problem of Equal Steps [Java]
  1273. Problem of Equal Steps II [Java]
  1274. Problem on a Pentagonal Star
  1275. Problem with angle bisector from 1975 Canadian Mathematical Olympiad
  1276. Problem with equal angles from 1987 IberoAmerican Mathematical Olympiad
  1277. Proclivity of Conjoint Archimedean Twins for Proliferation [JabvaScript, GeoGebra]
  1278. Projections of Convex Quadrilateral [JavaScript, GeoGebra]
  1279. Projections of Isogonal Conjugate are Concyclic [JavaScript, GeoGebra]
  1280. Projections on Internal and External Angle Bisectors [Java]
  1281. Projective Collinearity in a Quadrilateral [Java]
  1282. Projective infinity
  1283. Projective Invariants for Pascal And Desargues
  1284. Properties of Flank Triangles
  1285. Properties of the Circle of Similitude [Java]
  1286. Properties of Circle Through the Incenter
  1287. Properties of the Figures in Euclid I.47
  1288. Properties of the Harmonic Ratio
  1289. Property of 6-Parpolygon [Java]
  1290. Property of Angle Bisectors [Java]
  1291. Property of Circumscribed Quadrilaterals [Java]
  1292. Property of Points Where In- and Excircles Touch a Triangle [Java]
  1293. Property of Right Isosceles Triangle [Java, GeoGebra]
  1294. Property of Right Trapezoids [GeoGrebra]
  1295. Property of Semicircles [Java]
  1296. Property of Thébault Circles [JavaScript, GeoGebra]
  1297. Property of Two Pencils of Parallel Lines
  1298. Proportions and the Incenter [JavaScript]
  1299. Proportions in Square
  1300. Proportions with Two Orthocenters [JavaScript, GeoGebra]
  1301. Ptolemy's Theorem
  1302. Pure Angle Chasing [JavaScript, GeoGebra]
  1303. Pure Angle Chasing II [JavaScript, GeoGebra]
  1304. Pure Angle Chasing III [JavScript, GeoGebra]
  1305. Puzzles on graphs.
  1306. Pythagorean Theorem (121 proofs)
  1307. Pythagorean Perimeter Theorem
  1308. Pythagoras and Vecten Break Japan's Isolation [Java]
  1309. Pythagorean Triples [Java]
  1310. Quadrature: A Child's Play
  1311. Quadrilateral from a Segment
  1312. Quadrilateral Inequality
  1313. Quadrilateral Inscribed into Parallelogram
  1314. Quadrilateral With Equal Opposite Sides And Angles [Java]
  1315. Quadrilateral with 3 Equal Sides [Java]
  1316. Quadrilaterals Formed by Perpendicular Bisectors [Java]
  1317. Quest for Paragon [Java]
  1318. R and r When G on Incircle
  1319. Radical Axis and Center, an Application [Java]
  1320. Radical Axis of Circles Inscribed in a Circular Segment [Java]
  1321. Radical Center [Java]
  1322. Radius and Construction of a Mixtilinear Circle [Java]
  1323. Radius of a Circle by Paper Folding [Java]
  1324. Random Dot Stereograms [Java]
  1325. The Range of r/R in Triangle with Centroid on the Incircle
  1326. Ratios and Orthogonality in a Triangle - Problem from the 2006 Romania MO
  1327. Rational Points On a Circle
  1328. Rectangle Inscribed in Triangle [JavaScript, GeoGebra]
  1329. Rectified, Halved, Sheared, Eyeballs Still Surprise [JavaScript, GeoGebra]
  1330. Reflection in a Triangle Tangent to Parabola [JavaScript, GeoGebra]
  1331. Reflection In Line [Java]
  1332. Reflection in the Circumcenter
  1333. Reflections in Ellipse [Java]
  1334. Reflections of a Line Through the Orthocenter [Java]
  1335. Reflections of a Point on the Circumcircle [Java]
  1336. Reflections of the Orthocenter
  1337. Reflections of the Orthocenter [Java]
  1338. Reflections of the Orthocenter II Regular Hexagon and Triangle Joined at Vertex [JavaScript, GeoGebra]
  1339. Regular Hexagon from Arbitrary Triangle [JavaScript, GeoGebra]
  1340. Regular Octagon by Paper Folding
  1341. Regular Polygons in a Triangular Grid [Java]
  1342. Regular Polyhedra - Platonic Solids
  1343. Other Solids
  1344. Regular Pentagon Inscribed in Circle by Paper Folding
  1345. Regular polyhedra and Euler's Theorem
  1346. Reim's Similar Coins I
  1347. Reim's Similar Coins II
  1348. Reim's Similar Coins III
  1349. Reim's Similar Coins IV
  1350. Relation Engendered By Altitudes
  1351. Relation Engendered By Medians
  1352. Relations in a Cyclic Polygon
  1353. Remarkable Line in a Quadrilateral [Java]
  1354. Remarkable Line in Cyclic Quadrilateral [Java]
  1355. Rendezvous [Java]
  1356. Reverse Spoke Illusion [Java]
  1357. Revolving Circles Illusion [Java]
  1358. Rhombus in a Cyclic Quadrilateral [Java]
  1359. Rhombus in Circles [Java, GeoGebra]
  1360. Riemann Sphere and Möbius Transformation
  1361. Surprise: Right Angle in Circle [JavaScript, GeoGebra]
  1362. Surprising Length Dependence In Equilateral Triangle by Miguel Ochoa Sanchez
  1363. Right Triangles on Sides of a Square [Java]

    Rotating Square in Search of the Golden Ratio

  1364. Rotating Top Illusion [Java]
  1365. Rotating Gears [Java]
  1366. Rotation Transform [Java]
  1367. Rouse Ball's Fallacy [Java]
  1368. Rusty Compass Construction of Equilateral Triangle [Java]
  1369. Salinon: From Archimedes'Book of Lemmas [Java]
  1370. Sam Loyd's Geometric Puzzle
  1371. Sam Loyd's Son's Dissection [Java]
  1372. Sanchez's Areas in Bottema's Configuration [JavaScript]
  1373. Sangaku: Reflections and the Phenomenon
  1374. Sangaku: Critique of My View and a Response
  1375. Sangaku and The Egyptian Triangle
  1376. Sangaku in a Square
  1377. Sangaku Iterations, Is it Wasan? [Java]
  1378. Sangaku via Peru
  1379. Sangaku with 8 Circles
  1380. Sangaku with Angle between a Tangent and a Chord [Java]
  1381. Sangaku with Quadratic Optimization
  1382. Sangaku with Three Mixtilinear Circles [Java]
  1383. Sangaku with Versines [Java]
  1384. Sangakus with a Mixtilinear Circle [Java]
  1385. Scintillating Grid Illusion [Java]
  1386. Schwarz Lantern [Java]
  1387. Secant Angles [Java]
  1388. Secant Angles II [Java]
  1389. Secant, Normal, Tangent [Java]
  1390. Secant, Tangents and Orthogonality [Java]
  1391. See-Saw Lemma [Java]
  1392. Segment Projections in Equilateral Triangle
  1393. Segment Trisection [Java]
  1394. Segment Trisection II
  1395. Segment Trisection Induced by Parallels to Medians [Java]
  1396. Semicircle on Square [JavaScript]
  1397. Semi-regular Tessellation on Hinges A [Java]
  1398. Semi-regular Tessellation on Hinges B [Java]
  1399. Separating point sets with a circle
  1400. Sequences of Concyclic Points on a Conic
  1401. Sequences of Touching Circles
  1402. Serendipitous Beauty [Java]
  1403. Serendipitous Proofs Of The Pythagorean Theorem
  1404. Seven and the Eighth Circle Theorem
  1405. Seven Circles Theorem [Java]
  1406. Seven Concyclic Points [Java, GeoGebra]
  1407. Seven Equal Circles [JavaScript, GeoGebra]
  1408. Seven Problems in Equilateral Triangle
    1. Seven Problems in Equilateral Triangle, Solution to Problem 1
    2. Seven Problems in Equilateral Triangle, Solution to Problem 2
    3. Seven Problems in Equilateral Triangle, Solution to Problem 3
    4. Seven Problems in Equilateral Triangle, Solution to Problem 4
    5. Seven Problems in Equilateral Triangle, Solution to Problems 5, 6, 7
  1409. Seyran Ibrahimov's Inequality
  1410. Shaggy Dog Theorem
  1411. Shapes in a lattice
  1412. Shapes of constant width [Java]
  1413. Shearing and Translation in Pythagorean Pants [Java]
  1414. Shearing a Polygon into a Triangle of Equal Area [Java]
  1415. Shearing Butterflies in Quadrilaterals [Java]
  1416. Shedding Light on the Ball for Eyeballing
  1417. Shepard's Parallelogram Illusion [Java]
  1418. Shifted by the Inradius Tangent Collinearities [JavaScript, GeoGebra]
  1419. Shifting Cube Illusion [Java]
  1420. Shimmer Illusion [Java]
  1421. Short Construction of the Geometric Mean
  1422. Shortest Fence in a Quarter-Circle Pasture
  1423. Shredding the torus
  1424. Sides and Area of Pedal Triangle
  1425. Sierpinski Gasket By Common Trema Removal [Java]
  1426. Sierpinski Gasket Via Chaos Game [Java]
  1427. Sierpinski Gasket by Trema Removal [Java]
  1428. Similar Parallelograms on Sides of a Triangle
  1429. Similar Triangles And More
  1430. Similar Triangles in Crossing Circles [JavaScript, GeoGebra]
  1431. Similar Triangles on Sides of a Quadrilateral [Java]
  1432. Similar Triangles on Sides and Diagonals of a Quadrilateral [Java]
  1433. Similarity Is About Proportion - And Ways to Look at It
  1434. Simple Construction of the Circle of Apollonius
  1435. Simple dissection of an acute triangle
  1436. Simple Property of Circle Through the Incenter [JavaScript]
  1437. Simple Quadrilaterals Tessellate the Plane [Java]
  1438. Simson Line [Java]
  1439. Simsons and 9-Point Circles in Cyclic Quadrilateral [Java]
  1440. Simultaneous Contrast Illusion [Java]
  1441. Simultaneous Contrast Illusion II [Java]
  1442. Simultaneous Contrast: Koffka's Illusion [Java]
  1443. Simultaneous Contrast: White's Illusion [Java]
  1444. Simultaneous Contrast: White's Illusion, V-Variant [Java]
  1445. Three Concurrent Chords at 60 Degrees Angles
  1446. Simultaneous Diameters in Concurrent Circles [Java]
  1447. Simultaneous Generalization of the Theorems of Ceva and Menelaus
  1448. Sine and Cosine of 15 Degrees Angle
  1449. Sine, Cosine, and Ptolemy's Theorem
  1450. Six Circles with Concurrent Pairwise Radical Axes
  1451. Six Circles Theorem (Bui Quang Tuan) [Java]
  1452. Six Circles Theorem (Elkies) [Java]
  1453. Six Circles Theorem (Evelyn) [Java]
  1454. Six Concyclic Circumcenters in Fermat's Configuration [JavaScript, GeoGebra]
  1455. Six Concyclic Points [Java]
  1456. Six Concyclic Points on Sides of a Triangle
  1457. Six Concyclic Points II [Java]
  1458. Six Concyclic Points via Antipedal Triangle [JavaScript, GeoGebra]
  1459. Six Incircles in an Equilateral Triangle [Java]
  1460. Six Point Circle [Java]
  1461. SixPoints, ThreeLines [Java]
  1462. Soddy Circles and David Eppstein's Centers [Java]
  1463. Some Properties of Common Tangents [JavaScript, GeoGebra]
  1464. Some Properties of Napoleon's Configuration [Java]
  1465. Spectral Decomposition of a Planar Quadrilateral
  1466. Sperner's Lemma [Java]
  1467. Spiral Similarity [Java]
  1468. Spiral Similarity and CollinearitySpiral Similarity and Collinearity [Java, GeoGebra]
  1469. Spiral Similarity Leads to Equilateral Triangle [JavaScript, GeoGebra]
  1470. Square and Circle in a Gothic Cupola
  1471. Square from Four Points, One on Each Side
  1472. Square From Nowhere [Java]
  1473. Square in a Circle Inscribed in a Square [Java]
  1474. Square in a Right Triangle [Java]
  1475. Square in Chair [Java]
  1476. Square Inscribed in a Triangle [Java]
  1477. Square Inscribed in a Triangle II [Java]
  1478. Square, Similarity and Slopes [Java]
  1479. Squares and Straight Tetrominoes
  1480. Squares in Circles [Java]
  1481. Squares in Semicircle and Circle
  1482. Squares in Triangles
  1483. Squares Inscribed In a Triangle III [Java]
  1484. Squares on Sides of a Parallelogram [JavaScript, GeoGebra]
  1485. Squares on Sides of a Quadrilateral [Java]
  1486. Squares on Sides of a Quadrilateral II [JavaScript, GeoGebra]
  1487. Square out of a Quadrilateral
  1488. Squaring a circle
  1489. Squaring a Rectangle [Java]
  1490. Squinting Eyes Theorem [Java]
  1491. SSA
  1492. SSS
  1493. Staircase Illusion [Java]
  1494. Stan Fulger's Observation in Right Triangle
  1495. Star of David [Java]
  1496. Stathis Koutras' Butterfly
  1497. Stathis Koutras' Theorem
  1498. Stathis Koutras' Theorem II
  1499. Steiner's Circumellipse in Barycentric Coordinates [GeoGebra]
  1500. Steiner's Inellipse
  1501. Steiner's Sangaku
  1502. Steiner's Ratio Theorem
  1503. Steiner's Theorem
  1504. Stereographic Projection [Java]
  1505. Stereographic Projection and Inversion
  1506. Stereographic Projection and Radical Axes
  1507. Stewart's theorem
  1508. Straight Edge Only Construction of Polar
  1509. Structural Constellation [Java]
  1510. Sums of Squares in Circle
  1511. Sum of Squares in Equilateral Triangle
  1512. Sum of Squares of Distances to Vertices
  1513. Sum of Two Squares [JavaScript, GeoGebra]
  1514. Sums of Unit Vectors
  1515. Surprising 60° in Equilateral Triangle [JavaScript, GeoGebra]
  1516. Sylvester's Problem
  1517. Symmedians
  1518. Symmetries in a Triangle
  1519. Symmetries in Triangle II [JavaScript, GeoGebra]
  1520. Symmetry in an Asymmetric Configuration [JavaScript, GeoGebra]
  1521. (tan(72°)±tan( 60°)sin(30°$\mp$18°)= 1
  1522. Tangency Point of Two Circles [Java]
  1523. Tangent and Secant [Java]
  1524. Tangent as a Radical Axis [Java]
  1525. Tangent Circles, Similarity and Equal Segments [JavaScript, GeoGebra]
  1526. Tangent Circles and an Isosceles Triangle [Java]
  1527. Tangent Circles in a Parallelogram [Java]
  1528. Tangent, Cotangent and Square Roots Inequality
  1529. Tangent Curiosity in Equilateral Triangle [JavaScript, GeoGebra]
  1530. Tangent in Concurrency [Java]
  1531. Tangent Lines and Circles in Convex Quadrilateral [Java]
  1532. Tangent of 22.5° - Proof Wthout Words
  1533. Tangent to Circle in Three Steps
  1534. Tangent to the Incircle [JavaScript]
  1535. Tangent to two circles
  1536. Tangents And Bisectors
  1537. Tangents and Diagonals in Cyclic Quadrilateral [Java]
  1538. Tangents, Perpendiculars and Geometric Mean [Java]
  1539. Tarski-Banach Decompositions
  1540. Taylor circle [Java]
  1541. Terquem's Theorem [Java]
  1542. Tesseract [Java]
  1543. Tetrahedron in Parallelepiped
  1544. Tetrahedron with Equiareal Faces
  1545. Tetrahedron with Equiareal Faces, II
  1546. Tetrahedron with Orthogonal Perpendiculars to Opposite Edges
  1547. Thales' Theorem [Java, GeoGebra]
  1548. Thales' Theorems
  1549. Thales on Angle Bisectors [JavaScript, GeoGebra]
  1550. The 80-80-20 Triangle
  1551. The Beauty of Fractions
  1552. The Center of Gravity and Motion of Material Points [JavaScript, GeoGebra]
  1553. The Chaos Game: Address Space vs IFS [Java]
  1554. The Devil is in the Exceptions
  1555. The Eutrigon Theorem [Java, GeoGebra]
  1556. The Golden Pentacross
  1557. The Law of Cosines by Larry Hoehn
  1558. The Midpoint of an Angle Bisector - a Problem by A. A. Zaslavsky
  1559. The only rational triangle
  1560. The Pythagorean Theorem from a Combinatorial Identity
  1561. The Schwarz Lantern Explained [JavaScript]
  1562. The Shape of the Colosseum [Java, GeoGebra]
  1563. The Shortest Crease [JavaScript, GeeoGebra]
  1564. Thébault's Problem I [Java]
  1565. Thébault's Problem II [Java]
  1566. Thébault's Problem III [Java]
  1567. The Triangle of the Medians
  1568. Theorem of Complete Quadrilateral [Java]
  1569. Theorem of Three Tangents to a Conic [JavaScript, GeoGebra]
  1570. Theorems of Ceva and Menelaus, an Illustrated Generalization [Java]
  1571. There is no Difference Between Equilateral Triangles
  1572. Third Unusual Identity in Triangle
  1573. Three Circles and Area [JavaScript]
  1574. Three Circles and Common Tangents
  1575. Three Circles through the Incenter
  1576. Three Collinear and Four Concyclic Points [Java, GeoGebra]
  1577. Three Concurrent Circles [Java]
  1578. Three Common Chords in Three Concurrent Circles [Java, GeoGebra]
  1579. Three Congruent Circles by Reflection [Java]
  1580. Three Congruent Circles by Reflection II [Java]
  1581. Three Congruent Circles by Reflection III [Java]
  1582. Three Equal Circles in a Semicircle
  1583. Three Euler Lines That Are Four [JavaScript]
  1584. Three Incircles In a Right Triangle [Java]
  1585. Three Incircles in a Triangle [Java]
  1586. Three Isosceles Triangles [Java]
  1587. Three Orthogonal Circles Through Three Given Points [Java]
  1588. Three lines at 60 degres and Circumcenters [JavaScript, GeoGebra]
  1589. Three pairs of Parallel Lines and a Conic [JavaScript, GeoGebra]
  1590. Three Parabolas with Common Directrix [JavaScript,GeoGebra]
  1591. Three Parallels in a Triangle [Java]
  1592. Three Points on a Parabola [Java]
  1593. Three Pyramids are Better Than Two [Java]
  1594. Three regions sharing a common boundary
  1595. Three Similar Polygons [Java]
  1596. Three Similar Triangles [Java]
  1597. Three Similar Triangles II [Java]
  1598. Three Squares and Two Ellipses [Java]
  1599. Three Tangent Circles [Java]
  1600. Three Tangents, Three Chords in Ellipse [Java]
  1601. Three Tangent Circles Sangaku
  1602. Three Tangents Theorem [Java]
  1603. Three Tangents, Three Secants [Java]
  1604. Three Touching Circles [Java]
  1605. Three Travelers in Uniform Motion
  1606. Three visions of a fact [GeoGebra]
  1607. Tiling a Chessboard with Dominoes
  1608. Tiling Sphere by Four Equal Triangles
  1609. Toothpick Construction of a Square [Java]
  1610. Topological preliminaries
  1611. Torque as a Mathematical Object
  1612. Touching Circles [Java]
  1613. Touching Circles and Concurrency [Java]
  1614. Touching Circles with Given Centers II [Java]
  1615. Train wheel quandary
  1616. Transitivity in Action [Java]
  1617. Translated Triangles [Java]
  1618. Translation Transform [Java]
  1619. Transversal Trigonometry [JavaScript, GeoGebra]
  1620. Triangle ABC is right iff sin²A + sin²B + sin²C = 2
  1621. Triangle Area in Square with Incircle
  1622. Triangle Areas in a Parallelogram [Java]
  1623. Triangle Areas in a Parallelogram II [Java]
  1624. Triangle by HM segments [JavaScript, GeoGebra]
  1625. Triangle Classification [Java]
  1626. Triangle constructions and facts [Java]
  1627. Triangle Construction from Angle, Altitude and Median
  1628. Triangle from a, A, mc/mb
  1629. Triangle from Angle Bisector, Altitude and Circumradius
  1630. Triangle from Angle Bisector, Altitude and Inradius
  1631. Triangle from Inradius, Circumradius, Side or Angle
  1632. Triangle from Median, Altitude and Circumradius
  1633. Triangle from Side, Circumradius, and Median
  1634. Triangle from Angle, Inradius, and Difference of Sides
  1635. Triangle from Side, Inradius, and Altitude
  1636. Triangle from Side, Median, and Altitude
  1637. Triangle from Two Side Lines and the Euler Line
  1638. Triangle in a 4x4 Square
  1639. Triangle in a 5x5 Square
  1640. Triangle of Maximum Area
  1641. Triangle of Maximum Area II
  1642. Triangle of Minimum Perimeter [JavaScript]
  1643. Triangle on a Rectangular Hyperbola
  1644. Triangle Sliding on Two Straight Lines [Java]
  1645. Triangles, Squares and Areas from Temple Geometry [Java]
  1646. Triangles on HO
  1647. Triangles with Equal Area [Java]
  1648. Triangles with Sides in Geometric Progression [JavaScript]
  1649. Triangular Areas in Circle [JavaScript, GeoGebra]
  1650. Triangular Billiard [Java]
  1651. Triangulating Squares
  1652. Triangle with a 60 degrees angle [JavaScript, GeoGebra]
  1653. Trigonometry by Watching
  1654. Trigonometric Form of Ceva's Theorem [Java]
  1655. Trigonometric Functions [Java]
  1656. Trigonometric Identities with Arctangents
  1657. Trigonometric Identity for the Pi Day
  1658. Trigonometric Proof of the Pythagorean Theorem
  1659. Trigonometry According to Ptolemy
  1660. Trigonometry by Paper Folding
  1661. Trisect Segment: 2 Circles, 4 Lines
  1662. Trisectable angle that is not constructible
  1663. Tucker Circles [Java]
  1664. Tucker Circles Through Homothety [Java]
  1665. Twelve Matchsticks Area Puzzle
  1666. Twin Segments in Four Semicircles
  1667. Twins Beget Twins
  1668. Twisted Cord Illusion [Java]
  1669. Two Altitudes, One Midpoint
  1670. Two Arbelos, Two Chains
  1671. Two Cevians and Proportions in a Triangle
  1672. Two Circles, Two Segments - One Ratio
  1673. Two Circles and a Limit - Analytic Proof
  1674. Two Circles and One More [Java]
  1675. Two Circles and Two More [Java]
  1676. Two Circles, Ellipse, and Parallel Lines
  1677. Two Circles in a Parallelogram [Java]
  1678. Two Circles Inscribed in a Parallelogram [Java]
  1679. Two Circles in a Square [Java]
  1680. Two Circles in a Square II [Java]
  1681. Two Circles in an Angle [Java]
  1682. Two Circles on Angle Bisector [Java]
  1683. Two Circles on a Side of a Triangle [Java]
  1684. Two Circles, Tangents and Two Collinearities [JavaScript, GeoGebra]
  1685. Two Circumcircles And Two Pairs of Parallels [Java]
  1686. Two Circumcircles in Triangle [Java]
  1687. Two Conditions for a Triangle to Be Equilateral
  1688. Two coins puzzle
  1689. Two Congruent Circles by Reflection [Java]
  1690. Two Conics, Pascal, Chasles, and Cross-Ratio [JavaScript, GeoGebra]
  1691. Two Color Coloring of the Plane [Java]
  1692. Two Common Chords in Three Concurrent Circles [Java, GeoGebra]
  1693. Two Diameters and Longest Common Chord [Java, GeoGebra]
  1694. Two Equilateral Triangles [Java]
  1695. Two Equilateral Triangles on Sides of a Square
  1696. Two Homotheties in a Parallelogram [Java]
  1697. Two Intersecting Circles [Java]
  1698. Two Lines - Two Circles [Java]
  1699. Two Pencils of Parallel Lines [JavaScript, GeoGebra]
  1700. Two Pairs of Parallel Lines in a Triangle [Java, GeoGebra]
  1701. Two Parallels in a Triangle and One More [Java]
  1702. Two Pascals Merge into One [JavaScript, GeoGebra]
  1703. Two Perpendiculars From a Point to a Line [Java]
  1704. Two Planar Constructions Related to a 3D Problem
  1705. Two Perspective Triangles
  1706. Two Quadrilaterals [Java]
  1707. Two Quadruplets of Concyclic Points [JavaSCript,GeoGebra]
  1708. Two Quadruplets of Tangent Circles [Java]
  1709. Two Refinements of Ionescu-Weitzenbock Inequality
  1710. Two Regular Pentagons Joined at Vertex
  1711. Two Related Triangles of Equal Areas
  1712. Two Sangaku with Equal Incircles
  1713. Two Similar Triangles with Parallel Sides [JavaScript, GeoGebra]
  1714. Two Simsons in a Triangle [Java]
  1715. Two Squares and Another Square [Java]
  1716. Two Squares In Circle [JavaScript]
  1717. Two Symmetric Triangles Are Directly Decomposable [Java]
  1718. Two Touching Circles [Java]
  1719. Two Triangles Inscribed in a Conic [Java, GeoGebra]
  1720. Two Triangles Inscribed in a Conic - with Elementary Solution [Java, GeoGebra]
  1721. Two Triangles Inscribed in a Conic - with Solution [Java, GeoGebra]
  1722. Two Triangles With Common Base and Altitude [Java]
  1723. Two Triangles Sharing the Circumcenter
  1724. Two Triples of Concurrent Cevians and a Conic [JavaScript, GeoGebra]
  1725. Two Triples of Concurrent Circles [Java]
  1726. Two Triples of Similar Triangles [Java]
  1727. Uncommon Triangle Constructions
  1728. Unfolding Spirals Illusion [Java]
  1729. Urquhart's Theorem
  1730. USA 1975 Problem 4
  1731. Use of Homogeneous Coordinates for Geometrical Calculations
  1732. Van Aubel's Theorem for Quadrilaterals and Generalization
  1733. Van Khea's Fourth Identity in Triangle
  1734. Van Khea's Quickie
  1735. Van Obel Theorem, Determinants, and Barycentric Coordinates
  1736. Van Schooten's and Pompeiu's Theorems [Java]
  1737. Van Schooten's Locus Problem [Java]
  1738. Variations on the Theme of Tremas [Java]
  1739. Variations on the Theme of Tremas II [Java]
  1740. Varignon's Theorem, Proof Without Words
  1741. Varignon Parallelogram [Java]
  1742. Various Geometries
  1743. Vecten-Nikolin Hexagon [Java]
  1744. Vecten's Collinearity [Java]
  1745. Vecten's Mesh [Java]
  1746. Vector Addition and Subtraction [Flash]
  1747. Vector Algebra in Tetrahedron
  1748. Vector product
  1749. Versatile Theorem [Java]
  1750. Vertical and Horizontal Dominoes on a Chessboard
  1751. Vietnamese Extension of a Japanese Theorem [JavaScript]
  1752. Vietnamese Lemma towards an Extension of a Japanese Theorem [JavaScript, GeoGebra]
  1753. Viewing a Statue
  1754. Viviani's Theorem [Java]
  1755. Viviani's Theorem II [Java]
  1756. Viviani in Isosceles Triangle [Java]
  1757. Viviani by Inversion
  1758. Viviani by Vectors
  1759. Viviani's 3D Analogue
  1760. Sanchez's Viviani's Area Analogue [JavaScript, GeoGebra]
  1761. Volume and Area of Torricelli's Trumpet [JavaScript]

    Volume Inequality in Tetrahedron

  1762. Volume of Fibonacci Tetrahedron
  1763. Volume of Sphere and Volume of an Ellipsoid
  1764. Volumes of Two Pyramids
  1765. Wallace-Bolyai-Gerwien Theorem
  1766. Wallace's Theorem [Java]
  1767. Watt's and Chebyshev's Linkage [Java]
  1768. Weird curves bound normal areas
  1769. Weitzenbock by Sanchez
  1770. Weitzenböck Inequality [Java]
  1771. What does one see inside a spherical mirror? [Java]
  1772. What Is Analytic Geometry?
  1773. What Is Angle?
  1774. What Is Angle Chasing?
  1775. What Is Area?
  1776. What Is Ellipse?
  1777. What Is Indirect Proof?
  1778. What Is Line?
  1779. What Is Point?
  1780. When a Triangle is A-cute
  1781. When a Triangle is Equilateral [Java]
  1782. When Is Triangle Equilateral: Marian Dinca's Criterion
  1783. When Is Triangle Isosceles: Miguel Ochoa Sanchez's Criterion
  1784. When Two Segments Intersect? [JavaScript]
  1785. When index equals content [Java]
  1786. Wonderful Trigonometry In Equilateral Triangle
  1787. Why a Diameter Is the Longest Chord?
  1788. William Wallace's Proof of the Butterfly Theorem
  1789. William Wallace's 1803 Statement of the Butterfly Theorem [JavaScript, GeoGebra]
  1790. Wittenbauer's Parallelogram [Java]
  1791. Wundt Illusion [Java]
  1792. Wundt Block Illusion [Java]
  1793. Y. Sawayama's Lemma [Java]
  1794. Y. Sawayama's Theorem
  1795. YATPOPT, Yet Another Trigonometric Proof of the Pythagorean Theorem
  1796. Yet Another Appearance of the Golden Ratio [JavaScript, GeoGebra]
  1797. Yet Another Concurrence on the 9-Point Circle [JavaScript, GeoGebra]
  1798. Yet Another Seven Circles Theorem [JavaScript, GeoGebra]
  1799. Zaslavsky's theorem [Java]
  1800. Zöllner's Illusion [Java]

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