# Line associated with the symmedian point.

- Author:
- Anton Zakharov

M is the centroid of the triangle ABC
H is the orthocenter of the triangle ABC
L is the symmedian point (Lemoine point) of the triangle ABC
Z is constructed for points M and H by the method as defined here: https://math.stackexchange.com/questions/3748383/median-bisector
then,
Points L, Z, and one of the vertices of the triangle ABC apparently always lie on a line !
in this case L,Z,C are collinear. (conjecture)