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Math Help - Trouble finding center of a circle.

  1. #1
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    Trouble finding center of a circle.

    I have five points and Im trying to find the radius and center of the circle that contains these points.
    P1 (0,-229),
    P2 (129,-223)
    P3 (319,-184)
    P4 (457,-123)
    P5 (671,0)

    The equations I have been using so far:

    Slope1 = (y2 y1)/(x2 x1)
    Slope2 = (y3 y2)/(x3 x2)
    (Xcenter)Xc = (slope1*slope2(y1 y3)+slope2*(x1+x2)-slope1(x2-x3))/(2*(slope2-slope1)
    (Ycenter)Yc= -(1/Slope1)*(x-((x1+x2)/2))+((y1+y2)/2)
    R = sqrt((x1-Xc)^2+(y1-Yc)^2)

    Here is the problem that Im having if I use points 1,2, and 3 then the center is (16.4, 807.8). If I use Points 1, 2, and 4 then the center is (20.45, 720.9), and If I use points 1, 2, and 5 then the center is (101.25, 614.59). Now I know that the center of the circle is not moving, but according to my math it is. I know Im missing something can someone help, please?
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  2. #2
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    WHY 5 points? 3 points is all you need:

    Math Forum - Ask Dr. Math
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  3. #3
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    trouble finding center of circle

    Hi maximk,
    Your 5 points are in the fourth quadrant.I suggest that you use point 1 and 5 for one chord and 1 and two for second. Divide the dimensions by 10 to simplify calculations.You need to write two equations for thr perpendicular bisectors of each chord.Solve for x and y the center and then calculate the distance from center to any point.Multiply results by 10.


    bjh
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  4. #4
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    Yes you are correct. But to double check my work I tried out using different sets of 3 points. I figures since all the points come off the same circle the center should be the same no matter what combination of 3 out of the 5 points I use, right?
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  5. #5
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    bjh, I will give that a try.
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  6. #6
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    I tried using points 1, 2 and 1,5 and the center came out to be at (101,614). Now the question that I still have is why does the center change locations if I use other points? Am I making sense with my question? If all 5 points come from the edge of the circle, then the center (and radius) should be the same no matter what combination of the 5 points are used.

    Here is the problem that I’m having if I use points 1,2, and 3 then the center is (16.4, 807.8). If I use Points 1, 2, and 4 then the center is (20.45, 720.9), and If I use points 1, 2, and 5 then the center is (101.25, 614.59). Now I know that the center of the circle is not moving, but according to my math it is. I know I’m missing something can someone help, please?
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  7. #7
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    Hi Maximk,
    If the centers do not match the points do not lie on a circular arc.Point 1 and 5 do.Where did you get this question? It involves a lot of work with unusual numbers.


    bjh
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  8. #8
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    Well it’s for a project regarding dc generators. The points are specs for a particular limit that I’m trying to figure a formula for. But I was just recently informed that the points are off line segments. But with everyone’s help I was still able to represent the arc as a circle by choosing three points off several line segments and then drawing a circle. So my solutions are fairly close. But that also explains why I was not able to get a “stationary” center point. Thank you for everyone’s help.

    Max
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