Online Geometry Problem 622: Intersecting Circles, Concyclic Points, Centers, Radii. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows the intersecting circles A and B at points C and D. Line AC and circle B meet at E, line BC and circle A meet at F. Prove that the points A, E, F, B, and D are concyclic (lie on a same circle).