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Find the radius from a chord

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  • 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
    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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    • #3
      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?

      Comment


      • #4
        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 = (m + c)/2m

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        • #5
          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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          • #6
            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.

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            • #7
              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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              • #8
                Re: Find the radius from a chord

                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.

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                • #9
                  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.

                  roadbump

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                  • #10
                    Re: Find the radius from a chord

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

                    radius = (m + 1/4c)/2m

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

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                    • #11
                      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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                      • #12
                        Re: Find the radius from a chord

                        Yes, it's really works dear.



                        Originally posted by Unregistered
                        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

                        Comment


                        • #13
                          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 31-7/8" or 31.875. It crossed my points exactly. Thanks!

                          Ken

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                          • #14
                            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

                            Comment


                            • #15
                              Re: Find the radius from a chord

                              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.
                              [.. guest link removed ..]

                              Comment

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