Question 27
The diagonals of the parallelogram $ABCD$ intersect at $O$ and $M$ is the midpoint of the side $AB$. Let $P$ be a point of the segment $OC$ and $Q$ be the intersection of the lines $MP$ and $BC$. The parallel to $MP$ through $O$ intersects the line $CD$ at the point $N$. Prove that the points $A, N$ and $Q$ are collinear if and only if $P$ is the midpoint of the segment $OC$.