Problem 1096: Tangent Circles, Common Tangent, Chord, Radius, Center. Level: High School, SAT Prep, College Geometry

The figure below shows the equal circles O₁, O₂, and O₃ (radii r) with collinear centers and tangent at T₁ and T₂. Circle O (radius R) is tangent to circles O₁ and O₃ at C₁ and C₃, respectively. Chord AB passes through O₂ and is tangent to circles O₁ and O₃ at D₁ and D₃, respectively. Prove that AB = R + 3r.