Geometry Problem 993: Intersecting Circles, Secant, Tangent, Concyclic Points, Cyclic Quadrilateral, Perpendicular. Level: School, College

The circles O and Q intersect at A and B (see the figure) and CAD is a secant line. The tangents at C and D meet at E. CO ad DQ extended meet at F. Prove that (1) Points O, F, B, and Q are concyclic; (2) FB is perpendicular to EB.