Geometry Problem 67. Discover the Hidden Circle: Triangle, Circumcircle, Angles, Concyclic Points. Level: High School, SAT Prep, College

In a triangle ABC inscribed in a circle, B is the midpoint of arc DE, with D on arc AB and E on arc BC. Chord DE intersects AB at F and BC at G. Prove that points A, F, G, and C are concyclic (lie on the same circle). and angles CAG and CFG are congruent.
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Circle's secret found,
Points A,F,G,C in harmony align,
Prove concyclic bond.

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