Question 17
Let $ABC$ be a triangle, and $D, E$ the feet of the altitudes from $A$ and $B$, respectively. The line $(DE)$ meets the circumcircle of $ABC$ at two points $P$ and $Q$. Let $A'$, $B'$ be the reflections of $A$ and $B$ in $(BC)$ and $(AC)$, respectively. Show that $A'$, $B'$, $P$, $Q$ are concyclic.