Geometry Problem 1134:
Tangent Circles, Tangent Line, Triangle, Circumcircle,
Circumcenter. Level: High School, SAT Prep,
Honors Geometry, College, Math Education
Circles O1 and O2 are tangent at A (figure below).
BC is tangent to circle O1 at C. BD is tangent to circle O2 at
D. Prove that the circumcenter O3 of the triangle ACD lies on
the circumcircle O4 of triangle BCD.