Perimeter of Circle

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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:

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

$\blacksquare$


Sources