Geometry Problem 1581: Prove the Angle Bisection in a Cyclic Quadrilateral. Perfect for High School and College Students!

Let ABCD be a quadrilateral inscribed in a circle with center O. The extensions of AB and DC meet at E, and those of BC and DA meet at F. The circumcircle of triangle CDF intersects EF at G. Prove that the line GO bisects the angle BGD.

Geometry problem 1581 Geometry problem involving a cyclic quadrilateral inscribed in a circle, intersecting lines, and angle bisection