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.
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Find the radius from a chord
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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?

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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?
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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?
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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
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Re: Find the radius from a chord
Originally posted by UnregisteredAn 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
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.
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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 semicircular 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 semicircular 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.
roadbump
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Re: Find the radius from a chord
I am seeing your frustration. Please let me help you.
C= cord
H=height (sagitta)
solution #1: square one half of c
now divide by H
then add the value of H
finally divide by 2
DONE!!!
solution #2: Square C
now divide that by 8 times H
now Divide H by two and add
that to the former number.
solution #3: square H
multiply this by 4
Add to this, C squared
now divide all that by 8 times H
I sure hope this is helpful to find the radius of an arc knowing the cord length and the distance from the middle of the cord to the top of the arc
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Re: Find the radius from a chord
Yes, it's really works dear.
Originally posted by UnregisteredI am seeing your frustration. Please let me help you.
C= cord
H=height (sagitta)
solution #1: square one half of c
now divide by H
then add the value of H
finally divide by 2
DONE!!!
solution #2: Square C
now divide that by 8 times H
now Divide H by two and add
that to the former number.
solution #3: square H
multiply this by 4
Add to this, C squared
now divide all that by 8 times H
I sure hope this is helpful to find the radius of an arc knowing the cord length and the distance from the middle of the cord to the top of the arc
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Re: Find the radius from a chord
I just laid out formula #2 on the floor of my garage, and used a string to intersect my points. In my example C=27" & H=3". Using formula #2, the radius was 317/8" or 31.875. It crossed my points exactly. Thanks!
Ken
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I have the radius. I need to find the arc length within/above the chord.
Any simple formulas?
Practically speaking, I'm trying to find the length of an inside wall curve around an inside room corner. The over all corner angle (past the curved part) could be 90 degree, could be 45, or something else.
Yes, I could just measure it. But sometimes that's a bit difficult for one reason or another.
Thanks
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Re: Find the radius from a chord
Originally posted by UnregisteredYes 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?
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