Question 10
The diagonals $AC$, $BD$ of a convex quadrilateral $ABCD$ intersect at the point $O$. Let $M$, $N$ be the midpoints of the sides $AB$, $CD$ respectively. The point $P$ is chosen so that the quadrilateral $MONP$ is a parallelogram. Prove that the areas of the triangles $APD$, $BPC$ are equal.