#include <iostream>
#include <cmath>
using namespace std;

int main(){
    int x, y, x1, y1, x2, y2 , R1, R2;
    cout << "enter the x coordinate of the first
    circle: ";
    cin >> x1;
    cout << "enter the y coordinate of the first
    circle: ";
    cin >> y1;
    cout << "enter the radius of the first circle: ";
    cin >> R1;
    cout << "enter the x coordinate of the second
    circle: ";
    cin >> x2;
    cout << "enter the y coordinate of the second
    circle: ";
    cin >> y2;
    cout << "enter the radius of the second circle: ";
    cin >> R2;



    double x2c = x2 - x1;
    double y2c = y2 - y1;
    double c = ((R2 * R2) - (R1 * R1) - (x2c * x2c) -
    (y2c * y2c)) / 2 * x2c;
    double A = ((y2c * y2c) / (x2c * x2c)) + 1;
    double C = (c * c) - (R1 * R1);
    double B = 2 * C * (y2c / x2c);
    double d = sqrt(((x1 - x2) * (x1 - x2)) + ((y1 -
    y2) * (y1 - y2)));
    double D = B * B - 4 * A * C;

    if (d < R1 + R2){
    cout << "Circles Intersect" <<endl;
    float yi = ((-B + sqrt(D)) / 2 * A);
    float xi = ((C + (B + sqrt(D)) / 2 *A) * y2c) /
    x2c;
    cout << "x and y coordinates of first point of
    intersection intersection" << " " << xi << " " <<
    yi << endl;

    float xj = (-B - sqrt(D) /2 * A);
    float yj = ((C +(B - sqrt(D)) / 2 * A) * y2c) /
    x2c;
    cout << "x and y coordinates of first point of
    intersection intersection" << " " << xj << " " <<
    yj << endl;
    }
    else if (d == 0){
    cout << "circles are touching";
    float xi = ((C + (B + sqrt(D)) / 2 * A) * y2c) /
    x2c;
    float yi = (-B + sqrt(D)) / 2 * A;
    cout << "x and y cordinates of touching point are
    :" << " " << "(" << xi << "," << " " << yi << ")"
    << endl;
    }
    else if (R2 > (R1 * d) && (R1 * d) < abs(R1 - R2))
    {
    cout << "1st circle is inside the second";
    }
    else if(R1 > (R2 * d) && (R2 * d) < abs(R1 - R2)){
    cout << "Second circle is inside the first";
    }
    else if (d > (R1 + R2)){
    cout << "circles do not intersect";
    }


    return 0;
}