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Lemoine point (Definition)

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 $ABC$.

\includegraphics{lemoinep}
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 $L$.



"Lemoine point" is owned by drini. [ owner history (1) ]
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See Also: triangle, symmedian, Lemoine circle, incircle, centroid, incenter, Gergonne point, isogonal, isogonal conjugate, fundamental theorem on isogonal lines

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Cross-references: incentre, bisectors, medians, lines, Gergonne triangle, Gergonne point, centroid, isogonal conjugate, symmedians, point, intersection, triangle
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This is version 5 of Lemoine point, born on 2002-01-08, modified 2002-05-17.
Object id is 1448, canonical name is LemoinePoint.
Accessed 3906 times total.

Classification:
AMS MSC51-00 (Geometry :: General reference works )

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