## Three Tangents, Three Chords in Ellipse

The applet below offers an illustration to a statement which is a particular case of Pascal's Hexagon Theorem: given a triangle T_{1}T_{2}T_{3} inscribed in a non-degenerate conic. Let t_{1}, t_{2}, t_{3} be the tangents to the connic at points T_{1}, T_{2}, T_{3}. Then the points of intersection of T_{i}T_{j} with t_{k}

What if applet does not run? |

How does Pascal's theorem apply? Let the vertices of an inscribed hexagon coalesce in adjacent pairs producing a triangle with three sides of the hexagon degenerating into the tangents at the vertices of the so obtained triangle.

### 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 © 1996-2018Alexander Bogomolny

67081106