By a circle in $\mathbb{C}\cup \{\infty\}$, we mean a circle in plane $\mathbb{C}$ or a straight in $\mathbb{C}$ union with $\infty$.
Given two circles in $\mathbb{C}\cup \{ \infty\}$, does there exists a Möbius transformation $z\mapsto \frac{az+b}{cz+d}$ which takes these two circles to concentric circles?
(We can ask the same question by considering finitely many circles.)