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| Math Central | Quandaries & Queries |
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Question from prem: hello sir, i am engineer, i need the formula for calculate the arclength by using only chord length and radius only |
Prem,
The length of an arc of a circle is given by
arclength = r θ
where r is the radius of the circle and θ is the central angle measured in radians.
Suppose the length of the chord is c units. In the diagram below R is the midpoint of the chord.
sin(θ/2) = |QR|/|PQ| = c/(2r) and hence θ = 2 sin-1(c/(2r)). Thus
arclength = 2 r sin-1(c/(2r))
Harley
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