Go Geometry Problem Problem 289: Tangent circles, Radius, Perpendicular, Tangent

In the figure below, circles A (radius a) and B are tangent at C. AD is tangent to circle B and AE is perpendicular to AD.
If EF is tangent to circle B, prove that Tangent formula to prove. View or post a solution.
 

Tangent circles, radius
 

 
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