# incenter

The *incenter ^{}* of a geometrical shape is the center of the
incircle

^{}(if it has any). The radius of the incircle is sometimes called the

*inradius*.

On a triangle^{} the incenter always exists and it is the intersection^{}
point of the three internal angle bisectors. So in the next picture,
$AX,BY,CZ$ are angle bisectors^{}, and $AB,BC,CA$ are tangent to the
circle.

Title | incenter |

Canonical name | Incenter |

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

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

Owner | mps (409) |

Last modified by | mps (409) |

Numerical id | 11 |

Author | mps (409) |

Entry type | Definition |

Classification | msc 51M99 |

Synonym | incentre |

Related topic | Incircle |

Related topic | LengthsOfAngleBisectors |

Related topic | AngleBisectorAsLocus |

Related topic | Orthocenter^{} |

Related topic | Triangle |

Related topic | CevasTheorem |

Related topic | LemoinePoint |

Related topic | GergonnePoint |

Related topic | GergonneTriangle |

Related topic | TrigonometricVersionOfCevasTheorem |

Defines | inradius |