# centroid

The *centroid* of a triangle (also called *center of gravity* of
the triangle) is the point where the three medians intersect each other.

In the figure, $A{A}^{\prime},B{B}^{\prime}$ and $C{C}^{\prime}$ are medians and $G$ is the centroid of $ABC$. The centroid $G$ has the property that divides the medians in the ratio $2:1$, that is

$$AG=2G{A}^{\prime}\mathit{\hspace{1em}}BG=2G{B}^{\prime}\mathit{\hspace{1em}}CG=2G{C}^{\prime}.$$ |

Title | centroid |

Canonical name | Centroid |

Date of creation | 2013-03-22 11:55:44 |

Last modified on | 2013-03-22 11:55:44 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 11 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 51-00 |

Synonym | barycenter |

Synonym | center of gravity |

Related topic | Median |

Related topic | Orthocenter^{} |

Related topic | Triangle |

Related topic | EulerLine |

Related topic | CevasTheorem |

Related topic | CenterOfATriangle |

Related topic | LemoinePoint |

Related topic | GergonneTriangle |

Related topic | TrigonometricVersionOfCevasTheorem |