Sagitta

The perpendicular distance from an arc's midpoint to the chord across it, equal to the radius minus the apothem ,

(1)

For an arc of a circle having radius and chord length , the apothem is

(2)

so the sagitta is

(3)

Conversely, the radius can be recovered from the chord length and sagitta as

(4)

In coordinates centered at the midpoint of the chord, the height of the arc above the chord for is

(5)

and the arc length of the minor arc is

(6)

For a regular polygon of side length ,

			(7)
			(8)
			(9)
			(10)
			(11)

where is the circumradius, the inradius, is the side length, and is the number of sides.