Circle

Area of the circle = <math>\pi</math> × area of the shaded square

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 solutions to an equation of the form:

<math>x^2 + y^2 = r^2</math>

The measure of the line that forms the circle, or circumference, is given by:

<math>C = 2\pi*r</math>

The area inside the circle is calculated using the formula:

<math>A = \pi*r^2</math>

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 <math>r = 1</math> is called the unit circle, and is used extensively in trignometry.