Family of concentric circles

Definition

Consider a Euclidean plane and a point $p$ in the plane. The family of concentric circles centered at $p$ is the family of all the circles centered at $p$, along with the degenerate case of the radius zero circle, which is the point circle $p$.

This family yields a partition of the Euclidean plane into subsets, one of which is a point and the rest are nontrivial circles.