# lengths of triangle medians

By the Apollonius theorem^{}, in any triangle, the ${m}_{a}$, ${m}_{b}$, ${m}_{c}$ of the medians (http://planetmath.org/Median) of opposing the the sides $a$, $b$, $c$, respectively,
are

$${m}_{a}=\frac{1}{2}\sqrt{2{b}^{2}+2{c}^{2}-{a}^{2}},$$ |

$${m}_{b}=\frac{1}{2}\sqrt{2{c}^{2}+2{a}^{2}-{b}^{2}},$$ |

$${m}_{c}=\frac{1}{2}\sqrt{2{a}^{2}+2{b}^{2}-{c}^{2}}.$$ |

Title | lengths of triangle medians |
---|---|

Canonical name | LengthsOfTriangleMedians |

Date of creation | 2013-03-22 18:26:47 |

Last modified on | 2013-03-22 18:26:47 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 5 |

Author | pahio (2872) |

Entry type | Corollary |

Classification | msc 51M04 |

Synonym | lengths of medians |

Related topic | ProofOfApolloniusTheorem |

Related topic | CommonPointOfTriangleMedians |

Related topic | LengthsOfAngleBisectors |