Problem 443: Overlapping, Intersecting Circles, Common Chord, Secant line, Tangent line, Angles

The figure shows overlapping circles O and O' with the common chord AB and secant line CAD. Lines CE and AF are tangent to circle O. Lines AG and DE are tangent to circle O'. Prove that (1) angles BEC and BAG are congruent, (2) angles BED and BAF are congruent.