They are called equidistant points and form points on a sphere for a solid or a circle on a plane figure.
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A spherical surface, with its center at the given point, and its radius equal to the given distance.
They form the sphere whose center is the given point and whose radius is the given distance.
That's a figure called a "circle". The given distance is the circle's radius, and the point is its center.
It is a sphere.
circle, but the given end point is called the center of a circle : )