A sequence of circles which closes (such as a Steiner chain or the circles inscribed in the arbelos) is called a chain.
Chain of Circles
See also
Arbelos, Coxeter's Loxodromic Sequence of Tangent Circles, Nine Circles Theorem, Pappus Chain, Seven Circles Theorem, Six Circles Theorem, Steiner Chain, Steiner's PorismExplore with Wolfram|Alpha
References
Evelyn, C. J. A.; Money-Coutts, G. B.; and Tyrrell, J. A. "Chains of Circles." Ch. 3 in The Seven Circles Theorem and Other New Theorems. London: Stacey International, pp. 31-68, 1974.Referenced on Wolfram|Alpha
Chain of CirclesCite this as:
Weisstein, Eric W. "Chain of Circles." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChainofCircles.html