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Is there any formula to find radius of a circle segment if we know chordal legth and area of the segment?

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1 Answer 1

See http://en.wikipedia.org/wiki/Circular_segment.

We knew the chord's length is

$$ c = 2r\sin\frac\theta2 = r\sqrt{2-2\cos\theta} $$

and the area is

$$ A = \frac{r^2}2 (\theta - \sin\theta) $$

solving $R$ and $\theta$ for these two equations given $c$ and $A$ will give you the answer. But it is almost certain that you can only solve it numerically, since both $\theta$ and $\sin\theta$ are involved.

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