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#1
10-27-2006, 09:17 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, 10:23 PM
 Robert Fogt Administrator Join Date: Dec 2005 Location: Seattle, WA Posts: 3,416 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, 04:37 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, 04:23 AM
 Robert Fogt Administrator Join Date: Dec 2005 Location: Seattle, WA Posts: 3,416 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, 05:58 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
03-22-2007, 12:50 AM
 Robert Fogt Administrator Join Date: Dec 2005 Location: Seattle, WA Posts: 3,416 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
04-08-2007, 10:40 AM
 Unregistered Guest Posts: n/a
Re: Find the radius from a chord

An arch is in the form of a circle and has a span of 30 meters and height 10 m. What is the radius of arc.
May please give a solution for this
#8
04-08-2007, 12:30 PM
 Robert Fogt Administrator Join Date: Dec 2005 Location: Seattle, WA Posts: 3,416 Rep Power: 12
Re: Find the radius from a chord

Quote:
 Originally Posted by Unregistered An arch is in the form of a circle and has a span of 30 meters and height 10 m. What is the radius of arc. May please give a solution for this
You will also need to know the degree of the angle, which is Q in the above diagram.

The formula I have is:
XZ = Q * Pi/180 * r

You can solve the equation for r, and you know XZ, just need to know Q.
#9
04-25-2007, 06:45 AM
 Unregistered Guest Posts: n/a
Re: Find the radius from a chord

if you know only c, and m; what is the radius?

example, i'm standing on the out side of a semi-circular structure and i have no way of getting in to the interior to measure any angle. it is of such a nature that i can only measure a segment of the arc length of the semi-circular structure. i transfer that arc length to a piece of paper. i can now draw a chord of 'c' length and a can measure the sagitta (arc height from center point of chord or 'm'). what is the radius ?

what would be more useful is if i only know the arc length, what is the radius.

#10
04-25-2007, 12:04 PM
 Robert Fogt Administrator Join Date: Dec 2005 Location: Seattle, WA Posts: 3,416 Rep Power: 12
Re: Find the radius from a chord

If you know c and m, you can calculate the radius like so:

Knowing just the arc length XZ, you cant calculate the radius.

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