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Sagitta


Sagitta

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

 h=R-r.
(1)

For a regular polygon of side length a,

h=R-r
(2)
=1/2a[csc(pi/n)-cot(pi/n)]
(3)
=1/2atan(pi/(2n))
(4)
=rtan(pi/n)tan(pi/(2n))
(5)
=2Rsin^2(pi/(2n)),
(6)

where R is the circumradius, r the inradius, a is the side length, and n is the number of sides.


See also

Apothem, Chord, Circular Sector, Circular Segment

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Cite this as:

Weisstein, Eric W. "Sagitta." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Sagitta.html

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