Online Geometry Problem 607: Intersecting Circles, Triangles, Metric Relations, Measurement. Level: Mathematics Education, High School, College

The figure shows the intersecting circles A and B at points C and D. Line AC and circle B meet at E, line BC and circle A meet at F, and lines EF and AB meet at G. If AB = 10, EF = 4, and FG = 8, find the measure of BG.