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#1
10-27-2006, 08:17 PM
 Unregistered Guest Posts: n/a
Find the radius from a chord

By having only two measurments, first the length of the chord and the height of the curve, what is the formula for finding the radius of the circle.
#2
10-28-2006, 09:23 PM
 Robert Fogt Administrator Join Date: Dec 2005 Location: Seattle, WA Posts: 3,339 Rep Power: 12
Re: Find the radius from a chord

I am not exactly sure what you mean.

The chord meaures the curve of a sector of a circle? The height is what? The height from the center of the circle or the height from the ends of the chord?

I have a book listing many formulas, but none to help knowing just the length of the arc and the height.

Take a look at the following diagram, and point out all the information you know and I can supply the correct formula.

My guess is you know the height m and the arc length XZ. Is this correct?
#3
10-29-2006, 03:37 PM
 Unregistered Guest Posts: n/a
Re: Find the radius from a chord

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?
#4
11-01-2006, 03:23 AM
 Robert Fogt Administrator Join Date: Dec 2005 Location: Seattle, WA Posts: 3,339 Rep Power: 12
Re: Find the radius from a chord

Just to make sure we are talking about the same thing, c is a straight line between points X and Z, called the cord, the curved line would be called arc length XZ.

Assuming you know c (not XZ) and m then the formula would be:

r = (m² + ¼c²)/2m
#5
03-21-2007, 04:58 PM
 Unregistered Guest Posts: n/a
Re: Find the radius from a chord

I have the circle and a chord through the circle then i know the hight but how do i fing the radius? Does it have something to do with triangles and the hypotenuse?
#6
03-21-2007, 11:50 PM
 Robert Fogt Administrator Join Date: Dec 2005 Location: Seattle, WA Posts: 3,339 Rep Power: 12
Re: Find the radius from a chord

Using the image above, provide the symbols for what you know. I can look up the formula for what you need in my pocket ref. There is a section on circle segments, circle sectors, and circular zones.
#7
05-12-2011, 08:51 AM
 Unregistered Guest Posts: n/a
Re: Find the radius from a chord

Quote:
 Originally Posted by Robert Fogt Just to make sure we are talking about the same thing, c is a straight line between points X and Z, called the cord, the curved line would be called arc length XZ. Assuming you know c (not XZ) and m then the formula would be: r = (m² + ¼c²)/2m
brilliant, thankyou , i needed this info too. spot and many many thanks. Andy
#8
12-12-2007, 03:30 AM
 Unregistered Guest Posts: n/a
Re: Find the radius from a chord

Quote:
 Originally Posted by Unregistered Yes that is correct. I know the lenght of the chord (c) and the height of the arc created by the chord (m). Is there a formula to find the radius with this information?
Could you please let me know what the formula is by e mail.
#9
12-20-2007, 10:15 AM
 Mrs X can't count, can't spell! Join Date: Feb 2006 Location: New Zealand Posts: 2,294 Rep Power: 11
Re: Find the radius from a chord

Bumping for unregistered
#10
02-26-2008, 03:37 AM
 Unregistered Guest Posts: n/a
Re: Find the radius from a chord

I stumbled on this through a google search. I was also looking for the same formula which I couldnt find in any of my study books. It's in the machinist handbook but I dont have one here at home.

Here's the Formula R = ((C/2)² + H²)/2H

So in your case with a chord of 30m and a height of 10m

R = ((30/2)² + 10²)/2*10
R = ((225+100)/20
R = 325/20
R = 16.25m

I know I'm a little late on the thread but should help others.

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