# Stewart’s theorem

Let be given a triangle $\mathrm{\u25b3}ABC$ with $AB=c$, $BC=a$, $CA=b$, and a point $X$ on $BC$ such that $BX=m$ and $XC=n$. Denote with $p$ the length of $AX$.

Then

$$a({p}^{2}+mn)={b}^{2}m+{c}^{2}n.$$ |

Title | Stewart’s theorem |

Canonical name | StewartsTheorem |

Date of creation | 2013-03-22 11:44:07 |

Last modified on | 2013-03-22 11:44:07 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 11 |

Author | drini (3) |

Entry type | Theorem |

Classification | msc 51-00 |

Classification | msc 65-00 |

Classification | msc 81-00 |

Related topic | ApolloniusTheorem |

Related topic | CosinesLaw |

Related topic | ProofOfStewartsTheorem |

Related topic | StewartsTheorem |

Related topic | ProofOfApolloniusTheorem2 |