Family of concentric circles

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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.

Concentriccircles.png