A circle is the set of points in a plane that are equidistant from a given point $O$. The point $O$ is called the center/centre and the distance $r$ from this center/centre is called the radius. The double of the radius is called the diameter, $d$, i.e., $d = 2r$. The angle a circle subtends from its center/centre is a full angle, equal to $360^{\circ}$ or $2\pi$ radians.

The perimeter of a circle $C$ is called the circumference, and is given by

The area of a circle is given by

The equation of a circle with center/centre $\left(x_0,\,y_0\right)$ and radius $r$ in Cartesian coordinates is

The parametric equations of a circle with center/centre $\left(x_0,\,y_0\right)$ and radius $a$ can be given by

The polar coordinates of a circle with center/centre at the origin and radius $a$ is given by

The polar coordinates of a circle with center/centre at $\left(a,\,0\right)$ and radius $a$ is given by

The polar coordinates of a circle with center/centre at $\left(0,\,a\right)$ and radius $a$ is given by