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
 


Typography and Sketching of Problem 1432 using iPad Apps

Typography and Sketching of problem 1432 using iPad Apps, Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles