ISL 1996 G1

Let $ABC$ be a triangle, and $H$ its orthocenter. Let $P$ be a point on the circumcircle of triangle $ABC$ (distinct from the vertices $A$ , $B$ , $C$ ), and let $E$ be the foot of the altitude of triangle $ABC$ from the vertex $B$ . Let the parallel to the line $BP$ through the point $A$ meet the parallel to the line $AP$ through the point $B$ at a point $Q$ . Let the parallel to the line $CP$ through the point $A$ meet the parallel to the line $AP$ through the point $C$ at a point $R$ . The lines $HR$ and $AQ$ intersect at some point $X$ . Prove that the lines $EX$ and $AP$ are parallel.