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 T1T2T3 inscribed in a non-degenerate conic. Let t1, t2, t3 be the tangents to the connic at points T1, T2, T3. Then the points of intersection of TiTj with tk (i, j, k all different indices 1, 2, 3) are collinear.

 

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 http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


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

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

Copyright © 1996-2017Alexander Bogomolny

 61222154

Search by google: