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A sphere.

Q: What 3-dimensional figure is made from a set of points in space that are equidistant from a fixed point?

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It could be a circle or a sphere

A line in 2D and a plane in 3D A perpendicular bisector of the line connecting the 2 given points

I believe that is the definition of a straight line.

a globe.

A circle is a plane figure consisting of a curve in which every point is equidistant from a fixed point called the center.

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It could be a circle or a sphere

the set of points equidistant from a fixed point

A line in 2D and a plane in 3D A perpendicular bisector of the line connecting the 2 given points

It is a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).

The center of the circle. That's how the circle is defined. (The collection of all points on a plane equidistant from a fixed point. The fixed point is the center and the fixed distance is the radius.)

I believe that is the definition of a straight line.

A 'spherical' surface.

a sphere

Sphere

That set of points forms what is known as a "circle".

a globe.

A circle, rotated about any diameter, will generate a sphere with the same radius. A circle is the locus of all points in 2-dimensional space that are equidistant from a fixed point. A sphere is the locus of all points in 3-dimensional space that are equidistant from a fixed point.