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Math Help - Calculating four points on a circle

  1. #1
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    Calculating four points on a circle

    Hello,

    I have a tricky problem, and it has been years since Geometry.

    I need to calculate the points on and inner and outer circle based on a center line and a known Chord Length (L) and two know Radius (A, B)

    I am trying to locate A1, A2 and B1, B2


    Here is a diagram to help explain.


    Thanks

    Steve
    Attached Thumbnails Attached Thumbnails Calculating four points on a circle-ciclewithchords.jpg  
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  2. #2
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    Quote Originally Posted by sesproul View Post
    Hello,

    I have a tricky problem, and it has been years since Geometry.

    I need to calculate the points on and inner and outer circle based on a center line and a known Chord Length (L) and two know Radius (A, B)

    I am trying to locate A1, A2 and B1, B2


    Here is a diagram to help explain.


    Thanks

    Steve
    Use analytic geometry treating each circle separately where both circles are centered @ 0,0.
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  3. #3
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    I belive that I determines the solution using that method. Where I calc the Angle of Chord A (Div 2 using A and L) and Arc Sine, and then use that angle to calculate the hight of "Y" point using the Cosine of the angle, and A.

    Thanks


    Steve
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  4. #4
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    Quote Originally Posted by sesproul View Post
    Hello,

    I have a tricky problem, and it has been years since Geometry.

    I need to calculate the points on and inner and outer circle based on a center line and a known Chord Length (L) and two know Radius (A, B)

    I am trying to locate A1, A2 and B1, B2


    Here is a diagram to help explain.


    Thanks

    Steve
    Do you want coordinate (x,y) values for a circle centered at the origin? Or, do you want some ordinary (Euclidean) geometry construction? If the first, I'd use symmetry to advantage [Same above as below and as left is to right, so having found one, the rest follow form equal distances] If the second, I'd use a simple drafting program.

    For the first, a circle of radius "r", centered at the origin has an equation x^2 + y^2 = r^2 The chord is divided equally above and below the x-axis, so the distance to A1 for example would be L/2, where L is the length of the chord. That is the y-value. Sub that into the value for y and you have x^2 = r^2 - (L/2)^2 from which you can find the x-value.

    For the second, the only change is the radius length. If the first is r, the second could be R.
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