Question 173
Let $ABC$ be an acute triangle and $O$ the centre of its circumcircle. The line $OA$ meets the altitude $h_{b}$ at $P$ and the altitude $h_{c}$ at $Q$. Let $H$ be the orthocentre of triangle $ABC$. Prove that the centre of the circumcircle of triangle $PQH$ lies on the median of triangle $ABC$ through $A$.