What defines a circle?

A circle is defined as a set of points in a plane that are equidistant from a specific point known as the center. This means that every point on the perimeter of the circle maintains the same distance from the center. This distance is referred to as the radius of the circle. The definition emphasizes the relationship between the points of the circle and the center, which is fundamental in understanding the properties of circles in geometry.

In contrast, other definitions provided in the choices pertain to different geometric concepts. For instance, a line connecting two points on the circumference refers to a chord, which is a segment that does not encompass all points equidistant from the center. A polygon with equal sides describes a specific type of polygon, such as a regular polygon, rather than a circle. Lastly, the area inside a rectangular boundary pertains to rectangles or squares, not circles at all. Therefore, the definition of a circle consistently refers to the set of points equidistant from a center point, making it the correct answer.