# orthic triangle

If $ABC$ is a triangle and $AD,DE,CF$ are its three heights (http://planetmath.org/BaseAndHeightOfTriangle), then the triangle $DEF$ is called the *orthic triangle ^{}* of $ABC$.

A remarkable property of orthic triangles says that the orthocenter^{} of $ABC$ is also the incenter^{} of the orthic triangle $DEF$. That is, the heights of $ABC$ are the angle bisectors^{} of $DEF$.

Title | orthic triangle |

Canonical name | OrthicTriangle |

Date of creation | 2013-03-22 12:11:00 |

Last modified on | 2013-03-22 12:11:00 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 8 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 51-00 |

Related topic | Triangle |

Related topic | Orthocenter |

Related topic | EulerLine |

Related topic | CevasTheorem |

Related topic | CyclicQuadrilateral |

Related topic | TrigonometricVersionOfCevasTheorem |

Related topic | BaseAndHeightOfTriangle |