# Steiner’s theorem

Let $ABC$ be a triangle and $M,N\in (BC)$ be two points such that
$m(\mathrm{\angle}BAM)=m(\mathrm{\angle}NAC)$. Then the *cevians* $AM$ and $AN$ are
called isogonic cevians and the following relation holds:

$$\frac{BM}{MC}\cdot \frac{BN}{NC}=\frac{A{B}^{2}}{A{C}^{2}}$$ |

Title | Steiner’s theorem |
---|---|

Canonical name | SteinersTheorem |

Date of creation | 2013-03-22 13:21:41 |

Last modified on | 2013-03-22 13:21:41 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 6 |

Author | mathcam (2727) |

Entry type | Theorem |

Classification | msc 51N20 |