CN-TST 2014 Problem 1

$ABCD$ is a cyclic quadrilateral, with diagonals $AC,BD$ perpendicular to each other. Let point $F$ be on side $BC$ , the parallel line $EF$ to $AC$ intersect $AB$ at point $E$ , line $FG$ parallel to $BD$ intersect $CD$ at $G$ . Let the projection of $E$ onto $CD$ be $P$ , projection of $F$ onto $DA$ be $Q$ , projection of $G$ onto $AB$ be $R$ . Prove that $QF$ bisects $\angle PQR$ .