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Ratio of the distance between the centers of the circles and the point of intersection of two transverse common tangents to the circles

Given two circles, of given radii, such that the circles don’t touch each other. The task is to find the ratio of the distance between the centres of the circles and the point of intersection of two transverse common tangents to the circles.
Examples: 
 

Input :r1 = 4, r2 = 8 
Output :1:2

Input :r1 = 5, r2 = 13
Output :5:13


 


Approach
 



 

// C++ program to find the ratio
// of the distance between the centres of the circles
// and the point of intersection
// of two transverse common tangents
// to the circles which do not touch each other
 
#include <bits/stdc++.h>
using namespace std;
 
int GCD(int a, int b)
{
    return (b != 0 ? GCD(b, a % b) : a);
}
 
// Function to find the ratio
void ratiotang(int r1, int r2)
{
    cout << "The ratio is "
         << r1 / GCD(r1, r2)
         << ":"
         << r2 / GCD(r1, r2)
         << endl;
}
 
// Driver code
int main()
{
    int r1 = 4, r2 = 8;
    ratiotang(r1, r2);
    return 0;
}

                    
// Java program to find the ratio
// of the distance between the centres of the circles
// and the point of intersection
// of two transverse common tangents
// to the circles which do not touch each other
 
import java.io.*;
 
class GFG{
 
    static int GCD(int a, int b)
    {
        return (b != 0 ? GCD(b, a % b) : a);
    }
 
    // Function to find the ratio
    static void ratiotang(int r1, int r2)
    {
        System.out.println("The ratio is "
            + r1 / GCD(r1, r2)
            + ":"
            + r2 / GCD(r1, r2));
    }
 
    // Driver code
    public static void main (String[] args)
    {
        int r1 = 4, r2 = 8;
        ratiotang(r1, r2);
    }
}
 
// This code is contributed by NamrataSrivastava1

                    
# Python3 program to find the ratio
# of the distance between the centres of the circles
# and the point of intersection
# of two transverse common tangents
# to the circles which do not touch each other
 
def GCD(a, b):
    if(b!=0):
        return GCD(b, a%b);
    else:
        return a;
 
# Function to find the ratio
def ratiotang(r1, r2):
 
    print("The ratio is", r1 // GCD(r1, r2),
                     ":", r2 // GCD(r1, r2));
 
# Driver code
r1 = 4; r2 = 8;
ratiotang(r1, r2);
 
# This code is contributed by Code_Mech

                    
// C# program to find the ratio
// of the distance between the centres of the circles
// and the point of intersection
// of two transverse common tangents
// to the circles which do not touch each other
using System;
 
class GFG
{
 
    static int GCD(int a, int b)
    {
        return (b != 0 ? GCD(b, a % b) : a);
    }
 
    // Function to find the ratio
    static void ratiotang(int r1, int r2)
    {
        Console.WriteLine("The ratio is "
            + r1 / GCD(r1, r2)
            + ":"
            + r2 / GCD(r1, r2));
    }
 
    // Driver code
    static public void Main ()
    {
         
        int r1 = 4, r2 = 8;
        ratiotang(r1, r2);
    }
}
 
// This code is contributed by Tushil.

                    
<?php
// PHP program to find the ratio
// of the distance between the centres of the circles
// and the point of intersection
// of two transverse common tangents
// to the circles which do not touch each other
 
function GCD($a, $b)
{
    return ($b != 0 ? GCD($b, $a % $b) : $a);
}
 
// Function to find the ratio
function ratiotang($r1, $r2)
{
    echo "The ratio is ", $r1 / GCD($r1, $r2),
                     ":", $r2 / GCD($r1, $r2);
}
 
// Driver code
$r1 = 4;
$r2 = 8;
ratiotang($r1, $r2);
 
// This code is contributed by AnkitRai01
?>

                    
<script>
// javascript program to find the ratio
// of the distance between the centres of the circles
// and the point of intersection
// of two transverse common tangents
// to the circles which do not touch each other
function GCD(a , b)
{
    return (b != 0 ? GCD(b, a % b) : a);
}
 
// Function to find the ratio
function ratiotang(r1 , r2)
{
    document.write("The ratio is "
        + r1 / GCD(r1, r2)
        + ":"
        + r2 / GCD(r1, r2));
}
 
// Driver code
var r1 = 4, r2 = 8;
ratiotang(r1, r2);
 
// This code is contributed by Princi Singh
</script>

                    

Output: 
The ratio is 1:2

 

Time Complexity: O(log(min(a, b)))

Auxiliary Space: O(log(min(a, b)))


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