Problem 676: Circles, Diameter, Tangent, Chord, Metric Relations

The figure shows a circle O with diameter AB, BC is tangent to circle O at B. CA meets circle O at D. Circle of diameter AD meets AB at E. Circle of diameter AE meets AC at F. If AD = a, CD = b, and EF = x, prove that .

 
See also: Geometry problem 676: Typography in motion.