Q: What is formed when all points are equidistant from a central point?

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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.

A point is not a circle. A point has no dimensions, it is a single, exact location in space. A circle is defined as the set of all points equidistant from some central point.

All points on the circumference of a circle drawn on a plane are equidistant from the single point on the plane which is the center of the circle.

A circle

THE center

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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.

the set of points equidistant from a fixed point

A point is not a circle. A point has no dimensions, it is a single, exact location in space. A circle is defined as the set of all points equidistant from some central point.

circle

It is a point that is equidistant from the two end-points.

To find a point equidistant from three other points, construct perpendicular bisectors for two of the segments formed from three points. Note: this will be the center of the circle that has all three points on it's circumference. Three points, not in a straight line, form three pairs of points with each pair defining a different line. Take any pair of points and draw the perpendicular bisector of the line joining them. Repeat for one of the other pairs. These two perpendicular bisectors will meet at the point which is equidistant from all three points - the circumcenter of the triangle formed by the three points.

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

All points on the circumference of a circle drawn on a plane are equidistant from the single point on the plane which is the center of the circle.

sphere

A circle

THE center

A selection of some points on a circle.