Question:
Mobius Transformations for Circles
Prove: For any given circles R and R' in C_oo, there is a mobius transformation T such that T(r)=R'. Further, we can specify that T take any 3 points on R onto any 3 points of R'. If we do specify Tz_j for j=2,3,4 (distinct z_j in R), then T is unique.