# Thread: Trouble finding center of a circle.

1. ## Trouble finding center of a circle.

I have five points and I’m 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 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?

2. WHY 5 points? 3 points is all you need:

Math Forum - Ask Dr. Math

3. ## 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

4. 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?

5. bjh, I will give that a try.

6. 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?

7. 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

8. 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