Longitud de la tangente común directa entre dos círculos que se tocan externamente

Dados dos círculos, de radios dados, que se tocan externamente. La tarea es encontrar la longitud de la tangente común directa entre los círculos.
Ejemplos: 
 

Input: r1 = 5, r2 = 9
Output: 13.4164

Input: r1 = 11, r2 = 13
Output: 23.9165

Acercarse 
 

• Sean los radios r1 y r2 respectivamente.
• Dibuja una línea O paralela a PQ
• ángulo OPQ = 90 grados 
  ángulo O’QP = 90 grados 
  { la línea que une el centro del círculo con el punto de contacto forma un ángulo de 90 grados con la tangente }
• ángulo OPQ + ángulo O’QP = 180 
  OP || código QR
• Dado que los lados opuestos son paralelos y los ángulos interiores son 90, entonces OPQR es un rectángulo.
• Entonces OP = QR = r1 y PQ = OR = r1+r2
• En el triángulo OO’R
  ángulo ORO’ = 90 
  Por el teorema de Pitágoras
  OR^2 + O’R^2 = OO’^2 
  OO’^2 = (r1+r2)^2 + (r1-r2)^2
• Entonces, OO’ = 2√(r1*r2) 
  
   

A continuación se muestra la implementación del enfoque anterior: 
 

// C++ program to find the length of the direct
// common tangent between two circles
// which externally touch each other
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the length
// of the direct common tangent
void lengtang(double r1, double r2)
{
    cout << "The length of the "
         << "direct common tangent is "
         << 2 * sqrt(r1 * r2) << endl;
}
 
// Driver code
int main()
{
    double r1 = 5, r2 = 9;
    lengtang(r1, r2);
    return 0;
}

// Java program to find the length of the direct
// common tangent between two circles
// which externally touch each other
class GFG
{
 
    // Function to find the length 
    // of the direct common tangent
    static void lengtang(double r1, double r2)
    {
        System.out.println("The length of the "
                + "direct common tangent is "
                + (2 * Math.sqrt(r1 * r2)));
    }
 
    // Driver code
    public static void main(String[] args)
    {
        double r1 = 5, r2 = 9;
        lengtang(r1, r2);
    }
}
 
// This code contributed by Rajput-Ji

# Python3 program to find the length
# of the direct common tangent
# between two circles which
# externally touch each other
 
# Function to find the length
# of the direct common tangent
def lengtang(r1, r2):
    print("The length of the direct",
                 "common tangent is",
             2 * (r1 * r2)**(1 / 2));
 
# Driver code
r1 = 5; r2 = 9;
lengtang(r1, r2);
 
# This code contributed
# by PrinciRaj1992

// C# program to find the length of the direct
// common tangent between two circles
// which externally touch each other
using System;
 
class GFG
{
    // Function to find the length
    // of the direct common tangent
    static void lengtang(double r1, double r2)
    {
        Console.WriteLine("The length of the "
                + "direct common tangent is "
                + (2 * Math.Sqrt(r1 * r2)));
    }
     
    // Driver code
    static public void Main ()
    {
        double r1 = 5, r2 = 9;
        lengtang(r1, r2);
    }
}
 
// This code contributed by ajit.

<?php
// PHP program to find the length of the direct
// common tangent between two circles
// which externally touch each other
 
// Function to find the length
// of the direct common tangent
function lengtang($r1, $r2)
{
    echo "The length of the "
        , "direct common tangent is "
        , 2 * sqrt($r1 * $r2) ;
}
 
// Driver code
$r1 = 5; $r2 = 9;
lengtang($r1, $r2);
 
// This code is contributed by AnkitRai01
 
?>

<script>
 
// javascript program to find the length of the direct
// common tangent between two circles
// which externally touch each other
 
// Function to find the length 
// of the direct common tangent
function lengtang(r1 , r2)
{
    document.write("The length of the "
            + "direct common tangent is "
            + (2 * Math.sqrt(r1 * r2)).toFixed(5));
}
 
// Driver code
var r1 = 5, r2 = 9;
lengtang(r1, r2);
 
// This code contributed by Princi Singh
 
</script>

The length of the direct common tangent is 13.4164

Complejidad de tiempo: O(1)

Espacio Auxiliar: O(1)