Given two circles with one interior to the other, if small tangent circles can be inscribed around the region between the two circles such that the final circle is tangent to the first, the circles form a Steiner chain. The simplest way to construct a Steiner chain is to perform an inversion on a symmetrical arrangement on n circles packed between a central circle of radius b and an outer concentric circle of radius a. In this arrangement, sin(π/n) = (a - b)/(a + b), so the ratio of the radii for the small and large circles is b/a = (1 - sin(π/n))/(1 + sin(π/n)).

arbelos | Coxeter's loxodromic sequence of tangent circles | hexlet | Pappus chain | seven circles theorem | Steiner's porism