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