The circumference of a circle is divided into eight arcs by a convex quadrilateral ABCD, with
four arcs lying inside the quadrilateral and the remaining four lying outside it. The lengths of
the arcs lying inside the quadrilateral are denoted by p, q, r, s in counter-clockwise direction
starting from some arc. Suppose p + r = q + s. Prove that ABCD is a cyclic quadrilateral.