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.

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