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.