Question

which statement best defines a circle?
a. the set of all points in a plane that are the same distance from a given point called the center
b. the set of all points in a plane that are the same distance from each other surrounding a given point called the center
c. points in a plane that surround a given point called the center
d. the set of all points that are the same distance from a given point called the center

Explanation:

• Option A: A circle is defined as the set of all points in a plane (to specify the 2 - D context) that are equidistant (same distance) from a given point (the center). This matches the geometric definition.
• Option B: Points on a circle are not the same distance from each other (e.g., two points on a circle have different distances depending on their position), so this is incorrect.
• Option C: Just saying points surround the center is too vague and does not include the equidistant property, so it's wrong.
• Option D: It does not specify that the points are in a plane. A circle is a 2 - D figure, so the plane is an important part of the definition, making this incorrect.

Answer:

A. the set of all points in a plane that are the same distance from a given point called the center