To select the correct answer, let's examine each option closely:
OA: "points in a plane that surround a given point called the center" - This is not a precise definition because it does not specify the nature of "surrounding" relative to the center point.
OB: "the set of all points in a plane that are the same distance from a given point called the center" - This statement correctly defines a circle in mathematical terms. A circle is a set of points in a plane equidistant from a center point.
OC: "the set of all points that are the same distance from a given point called the center" - This statement is not completely accurate because it does not specify that the set of points must be "in a plane," which is essential to the definition of a circle.
OD: "the set of all points in a plane that are the same distance from each other surrounding a given point called the center" - This statement is incorrect because it describes a situation where every point is equidistant from every other point, which does not define a circle but rather an unbounded plane or perhaps a misunderstanding of a regular polygon.
The correct answer is OB: "the set of all points in a plane that are the same distance from a given point called the center." This definition includes all the essential elements of a circle:
1. A set of points (what the circle is made up of),
2. In a plane (a two-dimensional surface),
3. That are the same distance from a single point (equidistant),
4. The given point (known as the center of the circle).
Hence, the correct choice is answer OB.
