ISL 1966 Problem 28

In the plane, consider a circle with center $S$ and radius $1.$ Let $ABC$ be an arbitrary triangle having this circle as its incircle, and assume that $SA\leq SB\leq SC.$ Find the locus of

a.) all vertices $A$ of such triangles;

b.) all vertices $B$ of such triangles;

c.) all vertices $C$ of such triangles.