Surface of a sphere
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A sphere
In three dimensions, the solid defined as being bound by the set of points at a given distance form a point is a sphere. In two dimensions, the figure defined as being bound by the set of points at a given distance from a point is a circle. In one dimension, a line segment is bound by the two points at a given distance from a point.
A circle is the set of all the points that are the same (arbitrary) distance (called the radius) from some (arbitrary) point (called the center).
It is a circle or a sphere
A circle or a sphere would fit the given description.