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Generalizing (Posted on 2015-10-16) Difficulty: 4 of 5
If a triangle has two particular circles as its circumcircle and incircle, there exist an infinite number of other triangles with the same circumcircle and incircle.

Find a necessary and sufficient condition for such triangles to exist.

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts just offhand... | Comment 1 of 2
I'd think the triangle is equilateral, and the infinitely many other triangles are just rotations of the original, with the incircle and circumcircle concentric.
  Posted by Charlie on 2015-10-16 22:28:38
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