The Lemoine point of a triangle | plane geometry | advanced level

Episode 98.

The Lemoine point of a triangle | plane geometry | advanced level.

Branch of mathematics: plane geometry.
Difficulty level: advanced.

Definition. A symmedian $BM'$ of triangle $ABC$ in the line symmetrical to the median $BM$ with respect to the bisector $BD$.

Theorem. The symmedians of a triangle intersect at a single point (which is called the Lemoine point of that triangle).

Mathematics. Geometry. Plane geometry.
#Mathematics #Geometry #PlaneGeometry

tags:
mathematics,geometry,plane geometry,classical geometry,Euclidean geometry,triangle,line,circle,circumcircle,tangent,tangency point,symmedian,median,bisector,tangential,tangential triangle,symmetry,axis,Lemoine,Lemoine point

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