Geometry Problem 1432: Tangent Circles, Secant, Tangent Lines, Proportionality, Similarity

The figure below shows circle O1 and O2 tangent at T. Lines AB and CD pass through T. AE = a and CF = c are tangent to circle O2. BG = b and DH = d are tangent to circle O1. Prove that \({a \over c} = {b \over d}\).
 
 

Geometry Problem 1432: Tangent Circles, Secant, Tangent Lines, Proportionality, Similarity, Tutor

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