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: $$\frac{A_{sector}}{A_{cercle}}=\frac{A_{sector}}{\pi \cdot r^2}=\frac{\beta_{degrees}}{360^\circ} \\ \frac{I_{sector}}{perimetre}=\frac{I_{sector}}{2\pi \cdot r}=\frac{\beta_{degrees}}{360^\circ}$$

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