Školjka

%V0 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.