Problem 338. Triangle, Circumcircle, Inscribed Circle, Exterior angle bisector, Concyclic points. Level: High School, College, SAT Prep.

The figure shows a triangle ABC with the circumcircle O. A circle D is tangent to arc AC and side AC at E and F, respectively. BG is the exterior angle bisector of angle B. Prove that points B, F, E, and G are concyclic.