Problem 1099: Four Circles, Common External Tangent, Common Internal Tangent, Radius, Metric Relations, Sangaku. Level: High School, SAT Prep, College Geometry

The figure below shows the circles O₁ (radius r₁) and O₂ (radius r₂). A₁A₂ and B₁B₂ are the common external tangents and CD is a common internal tangent. Circle O₃ (radius r₃) touches A₁C, CD, and circle O₁. Circle O₄ (radius r₄) touches B₁D, CD, and circle O₁. Prove that .
 

See also:
Art and typography of problem 1099.