# medial triangle

The *medial triangle ^{}* of a triangle $\mathrm{\u25b3}ABC$ is the triangle formed by joining the midpoints

^{}of the sides of the triangle $\mathrm{\u25b3}ABC.$

Here, $\mathrm{\u25b3}{A}^{\prime}{B}^{\prime}{C}^{\prime}$ is the medial triangle.
The incircle^{} of the medial triangle is called the *Spieker circle* and the incenter^{} is called the *Spieker center*.
The circumcircle^{} of the medial triangle is called the *medial circle*.

An important property of the medial triangle is that the medial triangle $\mathrm{\u25b3}{A}^{\prime}{B}^{\prime}{C}^{\prime}$ of the medial triangle $\mathrm{\u25b3}DEF$ of $\mathrm{\u25b3}ABC$ is similar^{} to $\mathrm{\u25b3}ABC.$

Title | medial triangle |
---|---|

Canonical name | MedialTriangle |

Date of creation | 2013-03-22 13:11:17 |

Last modified on | 2013-03-22 13:11:17 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 8 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 51-00 |

Synonym | auxiliary triangle |

Defines | Spieker center |

Defines | Spieker circle |

Defines | medial circle |