Problem 532: Triangle, Circumcircle, Equal Angles, Perpendicular, Area. Level: High School, SAT, College Geometry

The figure shows a triangle ABC inscribed in a circle C₁. The angles ABD and CBE are congruent. DF is perpendicular to AB and DG is perpendicular to BC. If A₁, A₂, and A₃ are the areas of triangles EMN, AFM, and CGN, respectively, prove that A₁ = A₂ + A₃.