# Lemoine point

The Lemoine point of a triangle^{}, is the intersection^{} point of its three symmedians^{}. (That is, the isogonal conjugate^{} of the centroid).

It is related with the Gergonne point^{} by the following result:

On any triangle $ABC$, the Lemoine point of its Gergonne triangle is the Gergonne point of $ABC$.

In the picture, the blue lines are the medians, intersecting an the centroid $G$.
The green lines are anglee bisectors^{} intersecting at the incentre $I$ and the red lines are symmedians. The symmedians intersect at Lemoine point $L$.

Title | Lemoine point |

Canonical name | LemoinePoint |

Date of creation | 2013-03-22 12:11:02 |

Last modified on | 2013-03-22 12:11:02 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 9 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 51-00 |

Related topic | Triangle |

Related topic | Symmedian |

Related topic | LemoineCircle |

Related topic | Incircle^{} |

Related topic | Centroid |

Related topic | Incenter |

Related topic | GergonnePoint |

Related topic | Isogonal |

Related topic | IsogonalConjugate |

Related topic | FundamentalTheoremOnIsogonalLines |