To determine the best definition of a circle from the given options, we'll analyze each statement carefully.
Option A: "the set of all points in a plane that are the same distance from a given point called the center"
- This statement describes a circle accurately. A circle is indeed defined as all the points that are at a constant distance (radius) from a specific point (center) on the same plane.
Option B: "the set of all points that are the same distance from a given point called the center"
- This statement is close but misses an important detail. It does not specify that the points must lie in a plane, which is crucial for defining a circle.
Option C: "the set of all points in a plane that are the same distance from each other surrounding a given point"
- This statement is incorrect. It incorrectly describes the relationship between the points. A circle is not defined by the distance between the points themselves, but rather the distance from each point to the center.
Option D: "points in a plane that surround a given point called the center"
- This statement is very vague as it doesn't specify that the points are at a constant distance from the center. It implies a more general and less specific arrangement of points around a center.
Based on the above analysis, the best statement that defines a circle is clearly:
Option A: "the set of all points in a plane that are the same distance from a given point called the center".
Therefore, the answer is:
O A. the set of all points in a plane that are the same distance from a given point called the center.
