ÖMO 2007 Problem 4

Let $M$ be the intersection of the diagonals of a convex quadrilateral $ABCD$ . Determine all such quadrilaterals for which there exists a line $g$ that passes through $M$ and intersects the side $AB$ in $P$ and the side $CD$ in $Q$ , such that the four triangles $APM$ , $BPM$ , $CQM$ , $DQM$ are similar.