Q: Set of points equidistant from a given point?

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Sphere?

equidistant, the circumference of a circle is formed by equidistant points from the center of the circle. It could also be the surface of a sphere if you are not limited to two dimensions.

They are called equidistant points and form points on a sphere for a solid or a circle on a plane figure.

A circle is the set of all points in a plane that are equidistant from a given point, called the center.

A selection of some points on a circle.

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sphere

Circle!

a circle, centered at the given point.

circle

Sphere?

A locus of points is just the set of points satisfying a given condition. The locus of points equidistant from a point is a circle, since a circle is just a set of points which are all the same distance away from the center

the set of points equidistant from a fixed point

You can define a circle as the locus (set) of all points equidistant from a given point.

sphere

The set of all points in the plane equidistant from one point in the plane is named a parabola.

equidistant, the circumference of a circle is formed by equidistant points from the center of the circle. It could also be the surface of a sphere if you are not limited to two dimensions.

They are called equidistant points and form points on a sphere for a solid or a circle on a plane figure.