The figure below shows the equal circles O_{1},
O_{2}, and O_{3}
(radii r) with collinear centers and tangent at T_{1}
and T_{2}. Circle O (radius R) is tangent to circles O_{1}
and O_{3} at C_{1} and C_{3}, respectively. Chord
AB passes through O_{2} and is tangent to circles O_{1} and O_{3}
at D_{1}
and D_{3}, respectively. Prove that AB = R + 3r.
