# Euler line

In any triangle, the orthocenter^{} $H$, the centroid $G$ and the circumcenter^{} $O$ are collinear^{}, and $OG/GH=1/2$. The line passing by these points is known as the *Euler line ^{}* of the triangle.

This line also passes by the center of the nine-point circle^{} (or Feuerbach circle) $N$, and $N$ is the midpoint^{} of $OH$.

Title | Euler line |

Canonical name | EulerLine |

Date of creation | 2013-03-22 11:44:25 |

Last modified on | 2013-03-22 11:44:25 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 18 |

Author | drini (3) |

Entry type | Theorem |

Classification | msc 51-00 |

Classification | msc 58A05 |

Classification | msc 83E15 |

Classification | msc 83D05 |

Classification | msc 83E05 |

Classification | msc 83E50 |

Classification | msc 81-00 |

Classification | msc 83-00 |

Classification | msc 82-00 |

Related topic | Triangle |

Related topic | Orthocenter |

Related topic | Centroid |

Related topic | Collinear |

Related topic | Midpoint |

Related topic | OrthicTriangle |

Related topic | CenterOfATriangle |

Related topic | EulerLineProof |