void rotat(double x, double y, double &x1, double &y1, double ang){
    double vx = x1 - x;
    double vy = y1 - y;
    double nx = vx * cos(ang) - vy * sin(ang);
    double ny = vx * sin(ang) + vy * cos(ang);
    x1 = x + nx;
    y1 = y + ny;
}
pair<double, double> f(double x1, double y1, double a, double x2, double y2, double b, double ang){
    double c = sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
    rotat(x2, y2, x1, y1, ang);
    double vx = x1 - x2;
    double vy = y1 - y2;
    double nx = vx * b / c;
    double ny = vy * b / c;
    x1 = x2 + nx;
    y1 = y2 + ny;
    return {x1, y1};
}
pair<double, double> getCircle(double x1, double y1, double r1, double x2, double y2, double r2, double r, bool alternative = false){
    double a = r1 + r;
    double b = r2 + r;
    double c = sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
    double ang = acos((b * b + c * c - a * a) / (2 * b * c));
    if(alternative) return f(x1, y1, a, x2, y2, b, ang);
    else return f(x1, y1, a, x2, y2, b, -ang);
}