Problem 365. Circular Sector of 60 degrees, Midpoints, Perpendicular, Congruence. Level: High School, College, SAT Prep.

The figure shows a circular sector AOB of 60 degrees. C is a point on arc AB and points D, E, F, and G are the midpoints of AC, CB, OB, and OA, respectively. Prove that lines DF and EG are perpendicular.