Li C. Tien,  Three Pairs of Congruent Circles in a Circle,
Forum Geometricorum 4 (2004) 117--124.

Abstract:  Consider a closed chain of three pairs of congruent circles of radii a, b, c.   The circle tangent internally to each of the 6 circles has radius  R = a + b + c if and only if  there is a pair of congruent circles whose centers are on a diameter of the enclosing circle.   Non-neighboring circles in the chain may overlap.   Conditions for nonoverlapping are established. There can be a ``central circle'' tangent to four of the circles in the chain.

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