What is the algorithm for finding the center of a circle from three points?

Question

I have three points on the circumference of a circle:

pt A = (A.x, A.y);
pt B = (B.x, B.y);
pt C = (C.x, C.y);

How do I calculate the cente

Answer 1

public Vector2 CarculateCircleCenter(Vector2 p1, Vector2 p2, Vector2 p3)
{
    if (
        p2.x - p1.x == 0 ||
        p3.x - p2.x == 0 ||
        p2.y - p1.y == 0 ||
        p3.y - p2.y == 0
    ) return null;

    Vector2 center = new Vector2();
    float ma = (p2.y - p1.y) / (p2.x - p1.x);
    float mb = (p3.y - p2.y) / (p3.x - p2.x);
    center.x = (ma * mb * (p1.y - p3.y) + mb * (p1.x - p2.x) - ma * (p2.x + p3.x)) / (2 * (mb - ma));
    center.y = (-1 / ma) * (center.x - (p1.x + p2.x) * 0.5) + (p1.y + p2.y) * 0.5;
    return center;
}