KöMaL 2009 B4188

Sides $AB$ and $CD$ of a quadrilateral ABCD are not parallel. Let $E$ and $F$, respectively, be interior points of these sides. Prove that the midpoints of the line segments $AF$, $CE$, $BF$ and $DE$ form a convex quadrilateral whose area is independent of the choice of points $E$ and $F$.