BG-MO 1985 Problem 5

Let $P$ be a point on the median $CM$ of a triangle $ABC$ with $AC\ne BC$ and the acute angle $\gamma$ at $C$ , such that the bisectors of $\angle PAC$ and $\angle PBC$ intersect at a point $Q$ on the median $CM$ . Determine $\angle APB$ and $\angle AQB$ .