NL-NWO 1994 Problem 4

Let $P$ be a point on the diagonal $BD$ of a rectangle $ABCD$ , $F$ be the projection of $P$ on $BC$ , and $H \not= B$ be the point on $BC$ such that $BF=FH$ . If lines $PC$ and $AH$ intersect at $Q$ , prove that the areas of triangles $APQ$ and $CHQ$ are equal.