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Problem 565: Triangle, Isogonal lines, Angles, Congruence, Concyclic Points. Level: High School, SAT Prep, College

The figure shows a triangle ABC. Angles BAD and CAE are congruent and AD = AE. Angles ABF and CBG are congruent and BF = BG. Angles ACG and BCE are congruent and CE = CG. Prove that the points D, E, G, and F are concyclic (lie on a same circle).

Triangle, Isogonal lines, Congruence, Concyclic points
 

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