Question 8
The incircle of a scalene triangle $ABC$ touches the sides $\overline{AB}$ and $\overline{CA}$ at the points $M$ and $N$ respectively. The excircles opposite to vertices $B$ and $C$ touch the line $BC$ at points $P$ and $Q$ respectively. Prove that the quadrilateral $MNPQ$ is cyclic if and only if $\angle CAB = 90^\circ$.