# Family of concentric circles

From Diffgeom

## Definition

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

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