Let $ABC$ be an acute angled triangle and suppose $X$ is a point on the circumcircle of $\Delta ABC$ with $AX||BC$ and $X\neq A$. Denote by $G$ the centroid of triangle $ABC$, and by $K$ the foot of the altitude from $A$ to $BC$. Prove that $K,G,X$ are collinear.
I tried to apply Menelaus theorem but couldn't find a triangle to apply. I found a homothety centred at $G$ which maps the medial triangle to the main triangle. I guess the homothety maps $K$ to $X$ i.e. $K$ a point on the circumcircle of the medial triangle but i failed to proof this. Please help me.