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.