UA-UMO 1998 Problem 106

Let $AB$ and $CD$ be diameters of a circle with center $O$ . For a point $M$ on a shorter arc $CB$ , lines $MA$ and $MD$ meet the chord $BC$ at points $P$ and $Q$ respectively. Prove that the sum of the areas of the triangles $CPM$ and $MQB$ equals the area of triangle $DPQ$ .