Lemoine point

The Lemoine point of a triangleMathworldPlanetmath, is the intersectionMathworldPlanetmath point of its three symmediansMathworldPlanetmath. (That is, the isogonal conjugateMathworldPlanetmath of the centroid).

It is related with the Gergonne pointMathworldPlanetmath 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 bisectorsMathworldPlanetmath 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 IncircleMathworldPlanetmath
Related topic Centroid
Related topic Incenter
Related topic GergonnePoint
Related topic Isogonal
Related topic IsogonalConjugate
Related topic FundamentalTheoremOnIsogonalLines