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