 Steiner chain

A cyclic chain of distinct circles between two disjoint circle boundaries, each tangent to both boundaries and its two neighbours. In concentric coordinates with inner radius $\rho$ and outer radius $R$, the chain circles have radius $r=(R-\rho )/2$ and centre distance $d=(R+\rho )/2$. A simple disjoint chain with $n\ge 3$ closes when $r/d=\sin (\pi /n)$.

A Steiner chain is a geometric concept that refers to a particular arrangement of circles. Specifically, it is a sequence of circles that are tangent to each other and to some fixed line or point, along with the circles being arranged such that they share a common tangent at the points of tangency.