Finding Concentric Circles from Points

Question

I'm wondering if there is any elegant solution to the following problem. Consider $M$ points known to be on $N$ concentric circles. In addition, assume $M>N$. See the attached picture. Is there a known way of efficiently finding the center and fitting circles to these points? In the picture the points are on radial lines, but the question is for a general configuration of points on circles. As noted here the question does not have a unique solution in general. So, a refinement of this question would be, is there any $M>N$ for which the question has a unique solution? Also, is it possible to reformulate this as a least square problem (and use, for example SVD to solve)?

Answer 1

Consider the following:

Note that there are an infinite number of centers that satisfy your condition.

In this, $M=N+1,$ and there is no unique answer.

Maybe a rephrasing of your question would be solveable?