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

Printable View

- Apr 26th 2006, 06:19 AMaskmemathRadius 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 - Apr 26th 2006, 09:16 AMCaptainBlackQuote:

Originally Posted by**askmemath**

I am prepared to be proven wrong.

RonL - Apr 28th 2006, 01:12 PMThePerfectHacker
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,

$\displaystyle r\sin(s/2r)=2r-h$

----------------------

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 - Apr 28th 2006, 01:18 PMCaptainBlackQuote:

Originally Posted by**ThePerfectHacker**

The intersection chord theorem would give in this case:

$\displaystyle

n^2=h(2r-h)

$

surly?

RonL - Apr 29th 2006, 06:49 PMThePerfectHackerQuote:

Originally Posted by**CaptainBlack**

- Apr 29th 2006, 09:21 PMearbothQuote:

Originally Posted by**ThePerfectHacker**

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

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

Greetings

EB - Apr 29th 2006, 09:42 PMCaptainBlackQuote:

Originally Posted by**earboth**

RonL - Apr 30th 2006, 04:36 AMearbothQuote:

Originally Posted by**ThePerfectHacker**

Oh, PLEASE!

don't gamble with your rule nr. 5 :D

EB