In the plane, consider a circle with center
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
and radius
![1.](/media/m/f/6/7/f67f08c0471cbb9c2f13e29a08d9579d.png)
Let
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
be an arbitrary triangle having this circle as its incircle, and assume that
![SA\leq SB\leq SC.](/media/m/d/e/d/ded93ef145a376a8764c0a4f8620dd34.png)
Find the locus of
a.) all vertices
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
of such triangles;
b.) all vertices
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
of such triangles;
c.) all vertices
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
of such triangles.
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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.