Question 157
A triangle $ABC$ is given, with altitudes $AD$, $BE$ and $CF$, and orthocentre $H$. The segments $EF$ and $AD$ intersect at point $G$. The segment $AK$ is the diameter of the circumcircle of triangle $ABC$ and it intersects $BC$ at point $M$. Prove that the lines $GM$ and $HK$ are parallel. (Go Geometry)