Geometry Problem 1133: Circle, Chord, Tangent, Circumcircle, Similarity, Equal Product. Level: High School, SAT Prep, Honors Geometry, College, Math Education

In a circle O (figure below), chords AB and CD meet at E. F is a point on AB so that the tangent at E to the circumcircle of triangle DEF meets AC and CB extended at G and H, respectively. Prove that AF/FB = EG/EH.