OIM 1987 Problem 6

Let $ABCD$ be a convex quadrilateral and let $P$ and $Q$ be the points on the sides $AD$ and $BC$ respectively such that $\frac{AP}{PD}=\frac{BQ}{QC}=\frac{AB}{CD}$ . Prove that the line $PQ$ forms equal angles with the lines $AB$ and $CD$ .