# Circle

A **circle** is the set of all the points in a given plane that are the same distance, called the radius, *r*, from a given point called the center.

A circle may also be defined algebraically, as the set of solutions to an equation of the form:

- ,

where is the center of the circle.

The distance around the circle, or circumference, is given by:

The area inside the circle is calculated using the formula:

A circle is a conic section, the intersection of a plane with a cone such that the plane is perpendicular to the axis of the cone.

Circles can readily be constructed by using a fixed distance between a pencil point and the center. A compass is a tool for doing this easily.

A circle with is called the *unit circle*, and is used extensively in trigonometry.