Online Geometry Problem 829: Triangle, Circumcircle, Parallel, Chord,
Side, Metric Relations. Level: High School, College,
Mathematics Education

The figure below shows a triangle ABC with
circumcircle O and chord DE parallel to AC. BD and BE intersects AC at F
and G, respectively. If AB = 5, AF = 1, FG =3, and GC =2, find BC.