The proof depends on a property of the conjugation of inversions by other inversions (see ConjugateInversion.html ). Denote by Fa, Fb, etc. ... the inversions with respect to the circles a, b, ... etc. Then Fw is the inversion interchanging c and c* and we have (Fc*)(b*) = (Fw)(Fc)(Fw)(b*) = (Fw)(Fc)(b) = (Fw)(a) = a*. Thus the inversion (Fc*) interchanges circles a* and b* as stated.

Produced with EucliDraw© |