|Suppose that a circle C lies inside circle D, |
and that circle E touches both of them.
We can draw a sequence of circles, each touching C and D
and the previous member of the sequence.
There are two possibilities,
The proof is quite simple.
Note that C and D are non-intersecting i-lines.
Since the figure is symmetric about the common centre P,
it is clear that, if starting with E gives a Steiner Chain,
then starting with F will give the Steiner Chain obtained by rotation.
Clearly, it will contain the same number of circles.
The CabriJava pane on the right shows a typical Steiner Chain
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