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.