Saudi Arabian IMO Booklet

Let $B{B}_1$ and $C{C}_1$ be the altitudes of acute-angled triangle $ABC$, and $A_0$ is the midpoint of $BC$. Lines $A_0{B}_1$ and $A_0{C}_1$ meet the line passing through $A$ and parallel to $BC$ in points $P$ and $Q$. Prove that the incenter of triangle $P{A}_{0}Q$ lies on the altitude of triangle $ABC$.