ILL 1974 Problem 12

A circle $K$ with radius $r$ , a point $D$ on $K$ , and a convex angle with vertex $S$ and rays $a$ and $b$ are given in the plane. Construct a parallelogram $ABCD$ such that $A$ and $B$ lie on $a$ and $b$ respectively, $SA+SB=r$ , and $C$ lies on $K$ .