两个不相交圆的横向公切线长度

给定两个给定半径的圆，它们的中心相距给定的距离，这样两个圆就不会相互接触。任务是找到圆之间的横向公切线的长度。
例子：

Input: r1 = 4, r2 = 6, d = 12
Output: 6.63325

Input: r1 = 7, r2 = 9, d = 21
Output: 13.6015

方法：

1. 设圆的半径分别为r1和r2 。
2. 让中心之间的距离为d 个单位。
3. 画一条平行于 PQ 的线 O’R，
4. 角度 OPQ = 角度 RPQ = 90 度
   角度 O’QP = 90 度
   { 圆心与接触点的连线与切线成 90 度角 }
5. 角 RPQ + 角 O’QP = 180 度
   公关||奥克
6. 由于对边平行且内角为 90，因此O’PQR是矩形。
7. O’Q = RP = r2 和 PQ = O’R
8. 在三角形OO’R
   角度 ORO’ = 90 度
   根据毕达哥拉斯定理，
   OR^2 + O’R^2 = OO’^2
   O’R^2 = OO’^2 – OR^2
   O’R^2 = d^2 – (r1+r2)^2
   O’R^2 = √(d^2 – (r1+r2)^2)

$Length of transverse common tangent = sqrt((distance between centers)^2 - (sum of radii)^2)$

C++

// C++ program to find the length
// of the transverse common tangent
// between two circles which
// do not touch each other
 
#include 
using namespace std;
 
// Function to find the length
// of the transverse common tangent
void lengthOfTangent(double r1, double r2, double d)
{
 
    cout << "The length of the transverse"
         << " common tangent is "
         << sqrt(pow(d, 2) - pow((r1 + r2), 2))
         << endl;
}
 
// Driver code
int main()
{
    double r1 = 4, r2 = 6, d = 12;
    lengthOfTangent(r1, r2, d);
    return 0;
}

Java

// Java program to find the length
// of the transverse common tangent
// between two circles which
// do not touch each other
class GFG {
 
    // Function to find the length
    // of the transverse common tangent
    static void lengthOfTangent(double r1,
                                double r2, double d)
    {
 
        System.out.println("The length of the transverse"
                           + " common tangent is "
                           + Math.sqrt(Math.pow(d, 2)
                                       - Math.pow((r1 + r2), 2)));
    }
 
    // Driver code
    public static void main(String args[])
    {
        double r1 = 4, r2 = 6, d = 12;
        lengthOfTangent(r1, r2, d);
    }
}
 
// This code has been contributed by 29AjayKumar

Python3

# python 3 program to find the length
# of the transverse common tangent
# between two circles which
# do not touch each other
from math import sqrt, pow
 
# Function to find the length
# of the transverse common tangent
def lengthOfTangent(r1, r2, d):
    print("The length of the transverse",
                     "common tangent is",
          '{0:.6g}'.format(sqrt(pow(d, 2) -
                                pow((r1 + r2), 2))))
 
# Driver code
if __name__ == '__main__':
    r1 = 4
    r2 = 6
    d = 12
    lengthOfTangent(r1, r2, d)
     
# This code is contributed by
# Surendra_Gangwar

C#

// C# program to find the length
// of the transverse common tangent
// between two circles which
// do not touch each other
using System;
 
class GFG {
    // Function to find the length
    // of the transverse common tangent
    static void lengthOfTangent(double r1,
                                double r2, double d)
    {
 
        Console.WriteLine("The length of the transverse"
                          + " common tangent is "
                          + Math.Sqrt(Math.Pow(d, 2)
                                      - Math.Pow((r1 + r2), 2)));
    }
 
    // Driver code
    static public void Main()
    {
        double r1 = 4, r2 = 6, d = 12;
        lengthOfTangent(r1, r2, d);
    }
}
 
// This code has been contributed by ajit.

Javascript

 
// javascript program to find the length
// of the transverse common tangent
// between two circles which
// do not touch each other
 
 
// Function to find the length
// of the transverse common tangent
function lengthOfTangent(r1,r2 , d)
{
 
    document.write("The length of the transverse"
                       + " common tangent is "
                       + Math.sqrt(Math.pow(d, 2)
                                   - Math.pow((r1 + r2), 2)));
}
 
// Driver code
 
var r1 = 4, r2 = 6, d = 12;
lengthOfTangent(r1, r2, d);
 
// This code contributed by Princi Singh
 

输出：

The length of the transverse common tangent is 6.63325

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