"Concentric circle" division.

Given the coordinates of 3 points, how to find the center of the circle formed by these points with high precision. For achieving high precision,there must be any division process in it. Is there any way to do it?

• Answer:

  For the ultimate high precision, we can apply analytic geometry here. Now since you said you have coordinates, I suppose you have it laid out on the Cartesian plane. Try solving it by three equations with three unknowns. The general equation for circles is: x2+y2+Cx+Dy+E=0x2+y2+Cx+Dy+E=0x^2 + y^2 + Cx + Dy + E = 0 You have your coordinates with you and you now have 3 values for x, and 3 values for y. So plug them in to your general equation and solve for C, D and E. Now that you have your equation of the circle, you have to group the x variables and the y variables. You may transpose the constant, E on the right side of the equation. For each group x and y, do completing the square method. Remember that the numbers you add on the left must also be added on the right to attain equality. You may regroup and factor the left side of the equation which yields to this form (x−h)2+(y−k)2=r2(x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2 Take note that your h is your center's x coordinate, k is your center's y-coordinate, and r is your radius. Therefore, your center now is @ (h,k) --- for further understanding, grab an analytic geometry book now! ---