Question 82
Let $ABC$ be a triangle with $\angle ACB = 90^{\circ}$. The inscribed circle of $\triangle ABC$ touches sides $AC$ and $BC$ at $D$ and $E$, respectively. On the circumscribed circle of $\triangle ABC$, the midpoints of minor arcs $AC$ and $BC$ are respectively $P$ and $Q$. Prove that $D$, $E$, $P$, and $Q$ are all collinear.