Geometry Problem 1130: Cyclic Quadrilateral, Diagonals, Angle Bisector, Congruent Angles. Level: High School, SAT Prep, Honors Geometry, College, Math Education

In a cyclic quadrilateral ABCD, AC and BD meet at E, and AB and DC extended meet at F (figure below). G is on FE extended so that GE is the bisector of angle BGC. Prove that angles AGB and CGD are congruent.