These are chains of circles (sequence a0, a1, ...) tangent each to the previous and all to two circles c1, c2.
The problem here is to find the whole sequence given the two limiting circles and the first circle a0 of the chain.
A first solution is to consider the circle-bundle (I) generated by the circles c1, c2 and its orthogonal bundle (II). Then find circles d, d' ... of (II) tangent to a0 and invert a0 with respect to these circles. The construction of such circles d, d', ... is explained in TangentMember.html . By repeatedly applying this procedure one constructs arbitrary number of circles a1, a2, ... of the chain.
By the construction procedure we see that the points of mutual contact of the chain circles are on a circle f centered on O, which is the radical axis of every tripple of circle (a, b, c), where a, b are members of bundle (I) and c is a circle of the chain.
There is an easier way to obtain this chain of circles explained in SteinerChain2.html .
![[alogo]](alogo.png){kind=small}
Steiner chains of circles ![[0_0]](SteinerChain_files/SteinerChain_0_0_0.png)
![[0_1]](SteinerChain_files/SteinerChain_0_0_1.png)
![[0_2]](SteinerChain_files/SteinerChain_0_0_2.png)
![[1_0]](SteinerChain_files/SteinerChain_0_1_0.png)
![[1_1]](SteinerChain_files/SteinerChain_0_1_1.png)
![[1_2]](SteinerChain_files/SteinerChain_0_1_2.png)