Pascal’s mystic hexagram

If an hexagonMathworldPlanetmath ADBFCE (not necessarily convex) is inscribedMathworldPlanetmath into a conic (in particular into a circle), then the points of intersectionsMathworldPlanetmath of opposite sides (AD with FC, DBwith CE and BF with EA) are collinearMathworldPlanetmath. This line is called the Pascal lineMathworldPlanetmath of the hexagon.

A very special case happens when the conic degenerates into two lines, however the theorem still holds although this particular case is usually called Pappus theorem.

Title Pascal’s mystic hexagram
Canonical name PascalsMysticHexagram
Date of creation 2013-03-22 12:10:49
Last modified on 2013-03-22 12:10:49
Owner drini (3)
Last modified by drini (3)
Numerical id 10
Author drini (3)
Entry type Theorem
Classification msc 51-00
Synonym Pascal line
Synonym Pascal’s theorem
Related topic PappussTheorem