Problem 575: Cyclic quadrilateral, Angle bisector, Measurement.
Level: High School, College, Math Education.

The figure shows a cyclic quadrilateral ABCD. AB and DC meet at E, AD and BC meet at F. EG is the bisector of angle AED and FH is the bisector of angle AFB. If AH = 8, HB = 7, and AG = 4, find DG.