# butterfly theorem

Let $M$ be the midpoint^{} of a chord $PQ$ of a circle, through which two other chords $AB$ and $CD$ are drawn. If $AD$ intersects $PQ$ at $X$ and
$CB$ intersects $PQ$ at $Y$,then $M$ is also the midpoint of $XY.$

The theorem gets its name from the shape of the figure, which resembles a butterfly.

Title | butterfly theorem^{} |
---|---|

Canonical name | ButterflyTheorem |

Date of creation | 2013-03-22 13:10:06 |

Last modified on | 2013-03-22 13:10:06 |

Owner | giri (919) |

Last modified by | giri (919) |

Numerical id | 8 |

Author | giri (919) |

Entry type | Theorem |

Classification | msc 51-00 |