# Apollonius theorem

Let $a,b,c$ the sides of a triangle and $m$ the length of the median to the side with length $a$. Then ${b}^{2}+{c}^{2}=2{m}^{2}+\frac{{a}^{2}}{2}$.

If $b=c$ (the triangle is isosceles), then the theorem reduces to the
Pythagorean theorem^{},

$${m}^{2}+{(a/2)}^{2}={b}^{2}.$$ |

Title | Apollonius theorem^{} |

Canonical name | ApolloniusTheorem |

Date of creation | 2013-03-22 11:44:10 |

Last modified on | 2013-03-22 11:44:10 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 14 |

Author | yark (2760) |

Entry type | Theorem |

Classification | msc 51-00 |

Classification | msc 18-00 |

Classification | msc 81-00 |

Related topic | Triangle |

Related topic | Median |

Related topic | StewartsTheorem |

Related topic | ProofOfStewartsTheorem |

Related topic | ProofOfApolloniusTheorem2 |

Related topic | ParallelogramLaw |

Related topic | ProofOfParallelogramLaw |