Question 4
Let $C$ be a circle of radius $R$ and centre $O$, and $S$ a fixed interior point. 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 $M,N',M',N$ as $A$ moves around the whole circle.
