Let O be the circumcenter,R be the circumradius, and k be the circumcircle of a triangle ABC .
Let k1 be a circle tangent to the rays AB and AC, and also internally tangent to k.
Let k2 be a circle tangent to the rays AB and AC , and also externally tangent to k. Let A1 and A2 denote the respective centers of k1 and k2.
Prove that:
(OA1+OA2)2−A1A22=4R2. geometrycircumcirclegeometry proposed