IMO Shortlist 1966 problem 28


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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.
Izvor: Međunarodna matematička olimpijada, shortlist 1966