"Circle". That "same distance" is the radius of the circle, and that "given point" is the center of the circle.
The set of all points in a plane at a given distance from a given point.clock
A circle. However, that DOES depend on the Euclidean metric being used for measuring distance.
A circle or a sphere would fit the given description.
A circle is the set of all points in a plane at a given distance FROM a given point, which is known as the circle's center.
They are points on the circumference of a unique circle in the plane.
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the center.simplified, it is all the points on a plane that are the same distance from a given point.
That's a "circle". The given distance is the circle's radius, and the given point is the circle's center.
These point are usually called loci as they are defined by a give set of rules.