Question 181
Let $ABC$ be a triangle with a right angle at $C$. The bisector of $\widehat{BAC}$ meets $[BC]$ at $P$, and the bisector of $\widehat{ABC}$ meets $[AC]$ at $Q$. Let $M$ and $N$ be points on $[AB]$ such that $(MP)$ and $(NQ)$ are perpendicular to $(AB)$. What is the measure of the angle $\widehat{MCN}$?
