# Perimeter of Circle

## Theorem

The perimeter $C$ of a circle with radius $r$ is given by:

$C = 2 \pi r$

## Proof

By definition, the perimeter is the length of the circumference of the circle.

Let $C$ be the perimeter.

Then:

 $\ds \pi$ $=$ $\ds \frac C {2 r}$ Definition of $\pi$ (pi) $\ds \leadsto \ \$ $\ds C$ $=$ $\ds 2 \pi r$

$\blacksquare$