# Pascal’s mystic hexagram

If an hexagon^{} $ADBFCE$ (not necessarily convex) is inscribed^{} into a conic (in particular into a circle), then the points of intersections^{} of opposite sides
($AD$ with $FC$, $DB$with $CE$ and $BF$ with $EA$) are collinear^{}. This line is called the *Pascal line ^{}* 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 |