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)),
    };
}