Lemoine pointLemoinePoint2002-01-08 01:02:202002-05-17 02:48:25Definition\usepackage{graphicx}
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\newcommand{\figuraex}[2]{\begin{center}\includegraphics[#2]{#1}\end{center}}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 $ABC$.
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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 $L$.