function det(a, b, c, d, e, f, g, h, i) {
    return (a * e * i) + (b * f * g) + (c * d * h) - (a * f * h) - (b * d * i) - (c * e * g);
}

function circleFromPoints(p1, p2, p3) {
    const a = det(p1.x, p1.y, 1, p2.x, p2.y, 1, p3.x, p3.y, 1);
    const bx = -det(p1.x * p1.x + p1.y * p1.y, p1.y, 1, p2.x * p2.x + p2.y * p2.y, p2.y, 1, p3.x * p3.x + p3.y * p3.y, p3.y, 1);
    const by = det(p1.x * p1.x + p1.y * p1.y, p1.x, 1, p2.x * p2.x + p2.y * p2.y, p2.x, 1, p3.x * p3.x + p3.y * p3.y, p3.x, 1);
    const c = -det(p1.x * p1.x + p1.y * p1.y, p1.x, p1.y, p2.x * p2.x + p2.y * p2.y, p2.x, p2.y, p3.x * p3.x + p3.y * p3.y, p3.x, p3.y);

    return {
        x: -bx / (2 * a),
        y: -by / (2 * a),
        radius: Math.sqrt(bx ^ 2 + by ^ 2 - 4 * a * c) / (2 * Math.abs(a)),
    };
}