OMM 2003 Problem 4

The quadrilateral $ABCD$ has $AB$ parallel to $CD$ . $P$ is on the side $AB$ and $Q$ on the side $CD$ such that $\frac{AP}{PB}= \frac{DQ}{CQ}$ . M is the intersection of $AQ$ and $DP$ , and $N$ is the intersection of $PC$ and $QB$ . Find $MN$ in terms of $AB$ and $CD$ .