Advanced Euclidean Geometry

LeMoine Point
The symmedians of a triangle are concurrent at the
LeMoine point (also called the symmedian point).
This is a consequence of a more general result, namely:
Theorem: The isogonal conjugates of a set of
concurrent segments from the vertices to the opposite
sides of a triangle are also concurrent.
To prove this theorem we should recall the Law of
Sines for a triangle.