# 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