Tangency locus of a Steiner chain
= Tangency locus of a Steiner chain
{title2=$|z|=\sqrt{R\rho}$}
For a <Steiner chain> between concentric <circles>, tangencies of neighbouring <circles> are midpoints of their centres and lie on the <circle> of radius $\sqrt{R\rho}$. Under a <Möbius transformation>, their locus is a <generalized circle>, which may be a line. An ordinary-<circle> conclusion requires the pole of the inverse transformation to avoid the original locus.