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Which statement best defines a circle?

A. The set of all points in a plane that are the same distance from each other surrounding a given point called the center
B. Points in a plane that surround a given point called the center
C. The set of all points that are the same distance from a given point called the center
D. The set of all points in a plane that are the same distance from a given point called the center



Answer :

GinnyAnswer
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.

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