Find the radius from a chord

hi, i have a problem.. looking back at the first page of this post , the circle image,

how do i find the radius of the circle? just by using the height which is m and the curved line arc length XZ

hi looking back to the first page circle image, how do i find the radius just by using
m and the curved line arc length XZ?

[JohnS]

Originally Posted by Unregistered

hi looking back to the first page circle image, how do i find the radius just by using
m and the curved line arc length XZ?

See post #27 which sets up the equation.
But you have to solve a transcendental equation by iterative methods.

R= radius in meters
C= chord in meters
m= middle height in meters (heightfrom chord to top of arc)

R=C^/8m + m/2

C=10
m=.25

R= 10^/8(.25) + .25/2
R= 100/2 + 0.125
R= 50 + 0.125
R= 50.125 m

good luck.

Hi,thanks for this useful info.

One point though, does anyone not read the entire thread before posting????

The same question asked AND answered several times!

The answers are all there folks just read it.....

Originally Posted by Unregistered

Yes that is correct. I know the length of the cord (c) and the height of the arc created by the cord (m). Is there a formula to find the radius with this information?

What is the formula?

[JohnS]

Originally Posted by Unregistered

What is the formula?

See post #44 or numerous other posts in the thread.

Hi all!
I'm missing something that I have been looking at too long so I would appreciate some help
What if I know the Chord Length and the Radius or Diameter (Diameter of Corse being 2 * r)
I want to break it down into a usable example so here are some numbers to use
r = .625
c = .375
m = ?

Thanks!

[JohnS]

Originally Posted by Unregistered

Hi all!
I'm missing something that I have been looking at too long so I would appreciate some help
What if I know the Chord Length and the Radius or Diameter (Diameter of Corse being 2 * r)
I want to break it down into a usable example so here are some numbers to use
r = .625
c = .375
m = ?

Thanks!

From post #4
r = (m² + ¼c²)/2m

This results in the quadratic equation m² - 2*m*r + 0.25*c² =0, which has two solutions

m = r ± r*sqrt(1 - 0.25*c²/r²)

Normally, you want the solution with the minus sign. The chord divides a circle into two arcs, the first, less than 180°, has the m with the minus sign. The other piece of the circle, greater than 180°, the plus sign.

Substituing, the answer is 0.0288

The answer using the above Numbers should be 0.0288