Let ABCD be any convex quadrilateral and let P,Q,R,S be points on the segments AB,BC,CD, and DA, respectively. It is given that the segments PR and QS dissect ABCD into four quadrilaterals, each of which has perpendicular diagonals. Show that the points P,Q,R,S are concyclic.
geometrycyclic quadrilateralRMMRMM 2017