Program to determine the center and radius of the circle made by three given points

find-circle-center-and-radius.js

const findCircle = (point1, point2, point3) => {
    const x1 = point1.x
    const x2 = point2.x
    const x3 = point3.x
    const y1 = point1.y
    const y2 = point2.y
    const y3 = point3.y

    const x12 = (x1 - x2);
    const x13 = (x1 - x3);

    const y12 = (y1 - y2);
    const y13 = (y1 - y3);

    const y31 = (y3 - y1);
    const y21 = (y2 - y1);

    const x31 = (x3 - x1);
    const x21 = (x2 - x1);

    const sx13 = Math.pow(x1, 2) - Math.pow(x3, 2);
    const sy13 = Math.pow(y1, 2) - Math.pow(y3, 2);

    const sx21 = Math.pow(x2, 2) - Math.pow(x1, 2);
    const sy21 = Math.pow(y2, 2) - Math.pow(y1, 2);

    const f = ((sx13) * (x12)
        + (sy13) * (x12)
        + (sx21) * (x13)
        + (sy21) * (x13))
        / (2 * ((y31) * (x12) - (y21) * (x13)));
    const g = ((sx13) * (y12)
        + (sy13) * (y12)
        + (sx21) * (y13)
        + (sy21) * (y13))
        / (2 * ((x31) * (y12) - (x21) * (y13)));

    const c = -(Math.pow(x1, 2)) -
        Math.pow(y1, 2) - 2 * g * x1 - 2 * f * y1;

    // eqn of circle be
    // x^2 + y^2 + 2*g*x + 2*f*y + c = 0
    // where centre is (h = -g, k = -f) and radius r
    // as r^2 = h^2 + k^2 - c
    const h = -g;
    const k = -f;
    const sqr_of_r = h * h + k * k - c;

    // r is the radius
    const r = Math.sqrt(sqr_of_r);

    return {
        radius: r.toFixed(5),
        centre: {
            x: h,
            y: k,
        },
    }
}