Question 10
G1 (GBR) Let triangle $ABC$ have orthocenter $H$, and let $P$ be a point on its circumcircle, distinct from $A,B,C$. Let $E$ be the foot of the altitude $BH$, let $PAQB$ and $PARC$ be parallelograms, and let $AQ$ meet $HR$ in $X$. Prove that $EX$ is parallel to $AP$.