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.