Pascal's theorem

Pascal's theorem states that if an arbitrary hexagon is inscribed in any conic section, and opposite pairs of sides are extended until they meet, the three intersection points will lie on a straight line, the Pascal line of that configuration.

This theorem is the projective dual of Brianchon's theorem. It was discovered by Blaise Pascal when he was only 16 years old.

The theorem was generalized by Felix Möbius in 1847, as follows: suppose a polygon with $4n+2$ sides is inscribed in a conic section, and opposite pairs of sides are extened until they meet in $2n+1$ points. Then if $2n$ of those points lie on a common line, the last point will be on that line, too.