Question 62
Let $ABC$ be an acute triangle. The altitude from $A$ meets the circumcircle of $ABC$ again at $D$, and the altitude from $B$ meets the circumcircle of $ABC$ again at $E$. Line $(ED)$ meets sides $[AC]$ and $[BC]$ at $P$ and $Q$ respectively. Prove that $P, Q, B$ and $A$ are concyclic.