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Anachronist (talk | contribs) →Etc.: renamed and edited |
→Arc length and area: a in terms of c & R |
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The central angle is
:<math>
=== Chord length and height ===
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The area ''a'' of the circular segment is equal to the area of the [[circular sector]] minus the area of the triangular portion (using the double angle formula to get an equation in terms of <math>\theta</math>):
:<math>a = \tfrac{R^2}{2} \left(\theta - \sin \theta\right)</math>In terms of {{math|''c''}} and {{math|''R''}},
:<math>a = \tfrac{R^2}{2} \left(2\arcsin\tfrac{c}{2R} - \sin\left(2\arcsin\tfrac{c}{2R}\right)\right) = R^2\left(\arcsin\frac{c}{2R} - \frac{c}{2R}\sqrt{1-\left(\frac{c}{2R}\right)^2}\right)</math>
In terms of {{math|''R''}} and {{math|''h''}},
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