Online Geometry Problem 661: Intersecting Circles, Centers, Secant, Parallelogram. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows the intersecting circles O and O' at A and B. O'O extended and circle O meet at C. D is a point on circle O', DA and DB meet circle O at E and F, respectively. Prove that DECF is a parallelogram.