Problem 678: Triangle, Simson Line, Circumcircle, Tangent, Parallel, Perpendicular, Collinear Points. Level: High School, SAT, College Geometry

The figure shows a triangle ABC. The altitude AD meets the circumcircle O at E. Line GDF is the Simson line of E with respect to triangle ABC. Line AM is the tangent to circle O at A. Prove that line GDF is parallel to AM.