In geometry, how is a circle defined?

A circle is defined as a set of points in a plane that are all equidistant from a fixed point known as the center. This definition captures the essence of what a circle is: every point on the circumference of the circle is the same distance from the center, which is the defining characteristic of this geometric shape.

The distance from the center to the points on the circle is called the radius. This concept of equal distance is critical when identifying a circle, as it differentiates a circle from other geometric figures. The properties of a circle, including its circumference and area, are derived from this fundamental definition, allowing for various calculations and applications in geometry and beyond. Understanding this concept is essential for recognizing the defining features of not just circles, but also how they interact with other shapes and figures in the realm of geometry.