# incircle

The *incircle ^{}* or

*inscribed circle*of a triangle is a circle interior to the triangle and tangent to its three sides.

Moreover, the incircle of a polygon^{} is an interior circle tangent to all of the polygon’s sides. Not every polygon has an inscribed circle, but triangles always do.

The center of the incircle is called the incenter^{}, and it’s located at the point where the three angle bisectors^{} intersect.

If the sides of a triangle are $x$, $y$ and $z$, the area $A$ and the semiperimeter $p$, then the radius of incircle may be calculated from

$$r=\frac{2A}{x+y+z}=\frac{A}{p}=\sqrt{\frac{(p-x)(p-y)(p-z)}{p}}.$$ |

Title | incircle |

Canonical name | Incircle |

Date of creation | 2013-03-22 12:11:09 |

Last modified on | 2013-03-22 12:11:09 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 8 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 51M99 |

Related topic | LemoinePoint |

Related topic | Incenter |

Related topic | LemoineCircle |

Related topic | Triangle |

Related topic | GergonnePoint |

Related topic | GergonneTriangle |

Related topic | ConstructionOfTangent |