Online Geometry Problem 701: Intersecting Circles, Diameter, Perpendicular, Angles, Congruence. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows the intersecting circles O and O' at A and B. AB is the diameter of circle O', CD is perpendicular to AB and EDF is perpendicular to OD. Prove that angles ACF and BCE are congruent.