Geometry Problem 1134:
Tangent Circles, Tangent Line, Triangle, Circumcircle,
Circumcenter. Level: High School, SAT Prep,
Honors Geometry, College, Math Education

Circles O_{1} and O_{2} are tangent at A (figure below).
BC is tangent to circle O_{1} at C. BD is tangent to circle O_{2} at
D. Prove that the circumcenter O_{3} of the triangle ACD lies on
the circumcircle O_{4} of triangle BCD.