# Math Help - Radius from Arc

1. ## Radius from Arc

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

2. Originally Posted by askmemath
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
I don't think you will find a closed form solution for this problem - though
I am prepared to be proven wrong.

RonL

3. Here is a picture to help you out.
By the theorem of chord in a circle we have that,
$n^2=r(2r-h)$
But, $n=r\sin(s/2r)$
Thus, we have,
$r^2\sin(s/2r)=r(2r-h)$[/tex]
Thus,
$r\sin(s/2r)=2r-h$
----------------------
If you know calculus
Thus, you need to find the zero's of the function,
$f(x)=x\sin(s/2x)-2x+h$
Use Newton's method

4. Originally Posted by ThePerfectHacker
Here is a picture to help you out.
By the theorem of chord in a circle we have that,
$n^2=r(2r-h)$
Just as well that I checked my note on this problem

The intersection chord theorem would give in this case:

$
n^2=h(2r-h)
$

surly?

RonL

5. Originally Posted by CaptainBlack
Just as well that I checked my note on this problem

The intersection chord theorem would give in this case:

$
n^2=h(2r-h)
$

surly?

RonL
One thing that confuses me is how an immortal (me) makes such a mistake

6. Originally Posted by ThePerfectHacker
Here is a picture to help you out.
By the theorem of chord in a circle we have that,
$n^2=r(2r-h)$
But, $n=r\sin(s/2r)$
Thus, we have,
$r^2\sin(s/2r)=r(2r-h)$
...
Hello,

I'm a little bit confused: When you plug in the value of n, shouldn't be there a squared sine value too?:

$r^2\left(\sin(s/2r)\right)^2=r(2r-h)$

Greetings

EB

7. Originally Posted by earboth
Hello,

I'm a little bit confused: When you plug in the value of n, shouldn't be there a squared sine value too?:

$r^2\left(\sin(s/2r)\right)^2=r(2r-h)$

Greetings

EB
There should be, now how did I miss that (its in my notes)

RonL

8. Originally Posted by ThePerfectHacker
One thing that confuses me is how an immortal (me) makes such a mistake

Oh, PLEASE!

don't gamble with your rule nr. 5

EB