Please Help
If the arc length s and the distance h from the centre point of the associated chord to the arc is known, how do you calculate the radius?
Thank You
Here is a picture to help you out.
By the theorem of chord in a circle we have that,
$\displaystyle n^2=r(2r-h)$
But, $\displaystyle n=r\sin(s/2r)$
Thus, we have,
$\displaystyle r^2\sin(s/2r)=r(2r-h)$[/tex]
Thus,
$\displaystyle r\sin(s/2r)=2r-h$
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If you know calculus
Thus, you need to find the zero's of the function,
$\displaystyle f(x)=x\sin(s/2x)-2x+h$
Use Newton's method