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 T_iT_j with t_k (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 https://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

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