Online Geometry Problem 769: Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint of arc, Parallel to chord, Congruence. Level: High School, College, Mathematics Education

The figure shows a triangle ABC with the circumcenter O and the orthocenter H. M is the midpoint of arc AC, HD is parallel to BM (D on AC), OE is parallel to MA (E on AB), and OF is parallel to MC (F on BC). Prove that AE = ED = DF = FC. This entry contributed by Ajit Athle.