Given 3 points in the Cartesian plane, how can you find the coordinates of the center of the circle that intersects all three points, if there exists such a circle?

Answer 1

(A,B) (C,D) and ( E,F) are the 3 points

Per the distance formula, the radii from center (x,y) are

(x-A)^2 + (y-B)^2 = (x-C)^2 + (y-D)^2 = (x-E)^2 + (y-F)^2

Now you have three equations, but 6 undetermined coefficients.