UA-UMO 1997 Problem 107

In a parallelogram $ABCD$ , $M$ is the midpoint of $BC$ and $N$ an arbitrary point on the side $AD$ . Let $P$ be the intersection of $MN$ and $AC$ , and $Q$ the intersection of $AM$ and $BN$ . Prove that the triangles $BDQ$ and $DMP$ have equal areas.