两个外部接触的圆之间的直接公切线的长度

给定两个半径给定的圆，它们在外部相互接触。任务是找到圆之间的直接公切线的长度。
例子：

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

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

方法

• 让半径分别为r1和r2 。
• 画一条线OR平行于PQ
• 角度 OPQ = 90 度
  角度 O’QP = 90 度
  { 连接圆心和接触点的线与切线成 90 度角 }
• 角度 OPQ + 角度 O’QP = 180
  操作||二维码
• 由于对边平行且内角为90°，所以OPQR是一个矩形。
• 所以OP = QR = r1和PQ = OR = r1+r2
• 在三角形OO’R
  角度 ORO’ = 90
  根据毕达哥拉斯定理
  OR^2 + O’R^2 = OO’^2
  OO’^2 = (r1+r2)^2 + (r1-r2)^2
• 所以， OO’ = 2√(r1*r2)
  $length of the common tangent is = 2sqrt(r1*r2)$

下面是上述方法的实现：

C++

// C++ program to find the length of the direct
// common tangent between two circles
// which externally touch each other
 
#include 
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

// 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

# 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#

// 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.

Javascript

 
// 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
 

输出：

The length of the direct common tangent is 13.4164

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