The figure below shows
circle O_{1} and O_{2} tangent at T. Lines AB and CD pass
through T. AE = a and CF = c are tangent to circle O_{2}. BG = b
and DH = d are tangent to circle O_{1}. Prove that \({a \over c} = {b \over d}\).

## Typography and Sketching of Problem 1432 using iPad Apps