KöMaL 2016 C1340

Points $P$ , $Q$ , $R$ , $S$ lie on sides $AB$ , $BC$ , $CD$ , $DA$ of a rectangle $ABCD$ , respectively. Line segments $PR$ and $QS$ are perpendicular. Prove that the midpoints of line segments $SP$ , $PQ$ , $QR$ and $RS$ form a rectangle, which is similar to $ABCD$ .