Is there any formula to find radius of a circle segment if we know chordal legth and area of the segment?
Radius by chordal length and segment area
0
$\begingroup$
geometry
circles
1 Answers
2
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.