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