In geometry, a Steiner chain is a set of n circles, all of which are tangent to two given non-intersecting circles (blue and red in the top three images), where n is finite and each circle in the chain is tangent to the previous and next circles in the chain.
The 7 circles of this Steiner chain (black) are externally tangent to the inner given circle (red) but internally tangent to the outer given circle (blue).
The 7 circles of this Steiner chain (black) are externally tangent to both given circles (red and blue), which lie outside one another.
Seven of the 8 circles of this Steiner chain (black) are externally tangent to both given circles (red and blue); the 8th circle is internally tangent to both.
Soddy’s hexlet is a three-dimensional analog of the Steiner chain.
Source: mathmajik
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