Math: Geometry Problem 1003: Intersecting Circle, Circumcircle, Chord, Secant, Triangle, 90 Degree, Angle, Perpendicular Lines. Level: School, College.

The figure below shows circles O and Q intersecting at A and B. Chord CB extended meets circle O at C, chord CA extended meets circle O at E. Circumcircle of triangle CDE intersects circle Q at F. Prove that the measure of angle OFC is 90 degrees.