Concentric normalization of disjoint circles
= Concentric normalization of disjoint circles
Two disjoint ordinary <circle> boundaries can be taken to distinct concentric <circles> by a <Möbius transformation>. After their centres are put at $0,d$ with radii $a,b$, the map $(z-s)/(z-t)$ works when $st=a^2$ and $s+t=(d^2+a^2-b^2)/d$. Disjointness makes the quadratic have distinct real roots. Already concentric <circles> require no transformation.