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
and D3, respectively. Prove that AB = R + 3r.