The figure shows a triangle ABC inscribed in
a circle C_{1}. The angles ABD and CBE are congruent. DF is
perpendicular to AB and DG is perpendicular to BC. If A_{1}, A_{2}, and A_{3} are the
areas of triangles EMN, AFM, and CGN, respectively, prove that A_{1} = A_{2} +
A_{3}.
