IMO Shortlist 1966 problem 28
Dodao/la:
arhiva2. travnja 2012. In the plane, consider a circle with center
and radius
Let
be an arbitrary triangle having this circle as its incircle, and assume that
Find the locus of
a.) all vertices
of such triangles;
b.) all vertices
of such triangles;
c.) all vertices
of such triangles.
%V0
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
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