APMO 1995 Problem 4

Let $C$ be a circle with radius $R$ and centre $O$ , and $S$ a fixed point in the interior of $C$ . Let $AA'$ and $BB'$ be perpendicular chords through $S$ . Consider the rectangles $SAMB$ , $SBN'A'$ , $SA'M'B'$ , and $SB'NA$ . Find the set of all points $M$ , $N'$ , $M'$ , and $N$ when $A$ moves around the whole circle.