Q:

How to calculate the centre point of a circle given three points?

I am using Javascript and I know the positions of 3 points. I wish to use these to find out the center point of a circle.
I have found this logic (Not the chosen answer but the one with 11 upvotes) : https://math.stackexchange.com/questions/213658/get-the-equation-of-a-circle-when-given-3-points
But I can't seem to get my head around how to write the logic for it.
I can't use bounding box by the way, this has to be done using the three points :)
Any ideas ?

A:

My favorite resolution:
Translate the three points to bring one of them at the origin (subtract (X0,Y0)).
The equation of a circle through two points and the origin can be written 
2X.Xc + 2Y.Yc = X² + Y²

Plugging the coordinates of the two points, you get an easy system of two equations in two unknowns, and by Cramer
Xc = (Z1.Y2 - Z2.Y1) / D
Yc = (X1.Z2 - X2.Z1) / D

D = 2(X1.Y2 - X2.Y1), Z1 = X1²+Y1², Z2 = X2²+Y2²

to be translated back (add (X0,Y0)).

The formula fails when the three points are aligned, which is diagnosed by D = 0 (or small in comparison to the numerators).

        X1-= X0; Y1-= Y0; X2-= X0; Y2-= Y0;

        double Z1= X1 * X1 + Y1 * Y1;
        double Z2= X2 * X2 + Y2 * Y2;
        double D= 2 * (X1 * Y2 - X2 * Y1);

        double Xc= (Z1 * Y2 - Z2 * Y1) / D + X0;
        double Yc= (X1 * Z2 - X2 * Z1) / D + Y0;

