Pascal's Mystic Hexagram

Theorem
Let $ABCDEF$ be a hexagram whose $6$ vertices lie on an ellipse such that the order of vertices along the ellipse is $AECFBD$.


 * PascalsMysticHexagram.png

Then the points of intersection of the sides of $ABCDEF$ lie on a straight line.

Also see

 * Pappus's Hexagon Theorem
 * Desargues' Theorem
 * Pascal's Theorem