OMCC 2009 Problem 5

Given an acute and scalene triangle $ABC$ , let $H$ be its orthocenter, $O$ its circumcenter, $E$ and $F$ the feet of the altitudes drawn from $B$ and $C$ , respectively. Line $AO$ intersects the circumcircle of the triangle again at point $G$ and segments $FE$ and $BC$ at points $X$ and $Y$ respectively. Let $Z$ be the point of intersection of line $AH$ and the tangent line to the circumcircle at $G$ . Prove that $HX$ is parallel to $YZ$ .