To solve this question, we need to identify which statement best defines a circle. Let us carefully analyze each of the provided options:
Option A: "the set of all points that are the same distance from a given point called the center"
- This statement is mostly accurate but it does not specify that these points are in a plane.
Option B: "the set of all points in a plane that are the same distance from a given point called the center"
- This statement is precise and correctly encapsulates the definition of a circle. It defines a circle as all points in a plane that are equidistant from a particular point, known as the center.
Option C: "points in a plane that surround a given point called the center"
- This statement is incomplete and imprecise. It does not specifically state that the points are equidistant from the center.
Option D: "the set of all points in a plane that are the same distance from each other surrounding"
- This statement is incorrect as it suggests that the points are equidistant from each other, which is not the definition of a circle.
Given the analysis, it is clear that the statement that best defines a circle is Option B: "the set of all points in a plane that are the same distance from a given point called the center." This matches the standard mathematical definition of a circle.
Hence, the correct choice is:
- Option B.
