Question 170
Let $ABC$ be a triangle and let $D$, $E$ and $F$ be the feet of the altitudes from $A$, $B$ and $C$, respectively. Let $H$ be the orthocentre of triangle $ABC$. The segments $EF$ and $AD$ intersect at $G$. Let $K$ be the point on the circumcircle of triangle $ABC$ diametrically opposite to $A$. Let the line $AK$ meet $BC$ at $M$. Prove that the lines $GM$ and $HK$ are parallel.
