La Hire's Theorem in Ellipse: What Is It About?
A Mathematical Droodle

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Explanation

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Copyright © 1996-2018 Alexander Bogomolny

La Hire's Theorem in Ellipse

The applet suggests the following theorem:

Let there be two points A and B outside an ellipse. From points A and B draw tangents AC, AD, BE, BF to the ellipse. Then if B lies on CD, then A lies on EF.

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This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

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What if applet does not run?

This is just another illustration of a theorem valid for all non-degenerate conics.

Poles and Polars

• Poles and Polars
• Brianchon's Theorem
• Complete Quadrilateral
• Harmonic Ratio
• Harmonic Ratio in Complex Domain
• Inversion
• Joachimsthal's Notations
• La Hire's Theorem
• La Hire's Theorem, a Variant
• La Hire's Theorem in Ellipse
• Nobbs' Points, Gergonne Line
• Polar Circle
• Pole and Polar with Respect to a Triangle
• Poles, Polars and Quadrilaterals
• Straight Edge Only Construction of Polar
• Tangents and Diagonals in Cyclic Quadrilateral
• Secant, Tangents and Orthogonality
• Poles, Polars and Orthogonal Circles
• Seven Problems in Equilateral Triangle, Solution to Problem 1

Conic Sections > Ellipse

• What Is Ellipse?
  
• Analog device simulation for drawing ellipses
• Angle Bisectors in Ellipse
• Angle Bisectors in Ellipse II
• Between Major and Minor Circles
• Brianchon in Ellipse
• Butterflies in Ellipse
• Concyclic Points of Two Ellipses with Orthogonal Axes
• Conic in Hexagon
• Conjugate Diameters in Ellipse
• Dynamic construction of ellipse and other curves
• Ellipse Between Two Circles
• Ellipse in Arbelos
• Ellipse Touching Sides of Triangle at Midpoints
• Euclidean Construction of Center of Ellipse
• Euclidean Construction of Tangent to Ellipse
• Focal Definition of Ellipse
• Focus and Directrix of Ellipse
• From Foci to a Tangent in Ellipse
• Gergonne in Ellipse
• Pascal in Ellipse
• La Hire's Theorem in Ellipse
• Maximum Perimeter Property of the Incircle
• Optical Property of Ellipse
• Parallel Chords in Ellipse
• Poncelet Porism in Ellipses
• Reflections in Ellipse
• Three Squares and Two Ellipses
• Three Tangents, Three Chords in Ellipse
• Van Schooten's Locus Problem
• Two Circles, Ellipse, and Parallel Lines

|Activities| |Contact| |Front page| |Contents| |Geometry| |Eye opener|

Copyright © 1996-2018 Alexander Bogomolny