A chord of a circle divides the corresponding disk into two circular segments. The perimetre of a circular segment consists thus of the chord ($c$ ) and a circular arc ($a$ ).

The magnitude $r$ of the radius of circle and the magnitude $\alpha$ of a central angle naturally determine uniquely the magnitudes of the corresponding arc and chord, and these may be directly calculated from

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The area of a circular segment is obtained by subtracting from [resp. adding to] the area of the corresponding sector the area of the isosceles triangle having the chord as base [the adding concerns the case where the central angle is greater than the straight angle]: $$A \;=\; \frac{\alpha}{2\pi}\cdot\pi r^2\mp\frac{1}{2}r^2\sin\alpha \;=\;\frac{r^2}{2}(\alpha\mp\sin\alpha)$$

The height of the circular segment, i.e. the distance of the midpoints of the arc and the chord, may be expressed in the following forms: $$h \;=\; \left(1-\cos\frac{\alpha}{2}\right)r \;=\; r-\sqrt{r^2-\frac{c^2}{4}} \;=\; \frac{c}{2}\tan\frac{\alpha}{4}$$