= Steiner porism
{c}
= Steiner's porism
{c}
{synonym}
If a simple <Steiner chain> closes after $n\geq3$ <circles>, rotating the starting <circle> between concentric boundaries gives another closed $n$-<circle> chain. Applying a <Möbius transformation> proves the corresponding statement for arbitrary boundary <circles>. Construction must stay in the same intervening family and proceed without reversing the chosen direction. Merely choosing arbitrary <circles> tangent to the preceding <circle> permits backtracking and does not assert closure.
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