The circle

The perimeter of the circle is: $$P=2\cdot \pi r$$

The area of the circle is: $$A=\pi \cdot r^2$$

Using proportions it is possible to find the area of a circular sector and the length of the arc: $$\begin{gathered} \frac{A_{sector}}{A_{cercle}}=\frac{A_{sector}}{\pi \cdot r^2}=\frac{{\beta }_{degrees}}{{360}^{\circ }} \\ \frac{I_{sector}}{perimetre}=\frac{I_{sector}}{2\pi \cdot r}=\frac{{\beta }_{degrees}}{{360}^{\circ }} \end{gathered}$$

The same proportion can be used with $\beta$ in radians and changing ${360}^{\circ }$ for $2\pi$.