Go Geometry Problem Problem 313: Circle, Chord, Tangent, Perpendicular, Geometric Mean

The figure shows a circle O, a chord CD and a tangent at E. Lines CB and DA are perpendicular to AB. If EF is perpendicular to CD prove that EF is the geometric mean of BC and AD: Conclusion to prove.
 

Problem about tangent, chord, perpendicular
 

 
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