Problem 401. Area, Triangle, Angle bisector, Circumcircle, Perpendicular
bisector, Congruence. Level: High School, College, SAT Prep.
The figure shows a triangle ABC with
the circumcircle 1. CD is the angle bisector of angle C. FH is
the perpendicular bisector of BC and EG is the perpendicular
bisector of AC. Prove that triangles DGE, DHF, and CFG have
equal area.

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