To determine which statement best defines a circle, we need to recall the precise mathematical definition of a circle.
A circle is defined as the set of all points in a plane that are equidistant from a particular point called the center.
Now, let's evaluate each option provided:
A. 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 suggests points are the same distance from each other rather than from the center.
B. Points in a plane that surround a given point called the center.
- This statement is too vague and does not specify the equal distance criteria, which is crucial to the definition of a circle.
C. The set of all points that are the same distance from a given point called the center.
- This statement is close, but it is missing the specification that the points lie in a plane.
D. The set of all points in a plane that are the same distance from a given point called the center.
- This statement includes all necessary components: the points lie in a plane, they are equidistant, and it's from a given point called the center.
Given these evaluations, the correct answer is:
D. The set of all points in a plane that are the same distance from a given point called the center.
