两个相交圆的直接公切线长度

给定半径给定的两个圆，它们的中心相距给定的距离，使得这些圆在两点相交。任务是找到圆之间的直接公切线的长度。
例子：

Input: r1 = 4, r2 = 6, d = 3  
Output: 2.23607

Input: r1 = 14, r2 = 43, d = 35
Output: 19.5959

方法：

• 设圆的半径分别为r1和r2 。

• 让中心之间的距离为d 个单位。

• 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 度
  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 = d

• 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)
  或^2 + (r1-r2)^2 = d^2

• 所以， OR^2= d^2-(r1-r2)^2
  OR = √{d^2-(r1-r2)^2}
  $Length of the direct common tangent = sqrt((distancebetweencenters)^2 - (difference of radii)^2)$

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 intersect each other
#include 
using namespace std;
 
// Function to find the length of the direct common tangent
void lengtang(double r1, double r2, double d)
{
    cout << "The length of the direct"
         <<" common tangent is "
         << sqrt(pow(d, 2) - pow((r1 - r2), 2))
         << endl;
}
 
// Driver code
int main()
{
    double r1 = 4, r2 = 6, d = 3;
    lengtang(r1, r2, d);
    return 0;
}

Java

// Java program to find
// the length of the direct
// common tangent between two circles
// which intersect each other
class GFG
{
 
    // Function to find the length of
    // the direct common tangent
    static void lengtang(double r1, double r2, double d)
    {
        System.out.println("The length of the direct"
                + " 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 = 3;
        lengtang(r1, r2, d);
    }
}
 
/* This code contributed by PrinciRaj1992 */

Python3

# Python program to find
# the length of the direct
# common tangent between two circles
# which intersect each other
  
# Function to find the length of
# the direct common tangent
def lengtang(r1, r2, d):
    print("The length of the direct common tangent is "
        ,((d** 2) - ((r1 - r2)** 2))**(1/2));
 
  
# Driver code
r1 = 4; r2 = 6; d = 3;
lengtang(r1, r2, d);
 
# This code has been contributed by 29AjayKumar

C#

// C# program to find
// the length of the direct
// common tangent between two circles
// which intersect each other
using System;
 
class GFG
{
 
    // Function to find the length of
    // the direct common tangent
    static void lengtang(double r1, double r2, double d)
    {
        Console.WriteLine("The length of the direct"
                + " 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 = 3;
        lengtang(r1, r2, d);
    }
}
 
/* This code contributed by PrinciRaj1992 */

Javascript

 
// javascript program to find
// the length of the direct
// common tangent between two circles
// which intersect each other
 
// Function to find the length of
// the direct common tangent
function lengtang(r1 , r2 , d)
{
    document.write("The length of the direct"
            + " common tangent is "
            + (Math.sqrt(Math.pow(d, 2) -
                Math.pow((r1 - r2), 2))).toFixed(5));
}
 
// Driver code
var r1 = 4, r2 = 6, d = 3;
lengtang(r1, r2, d);
 
 
// This code contributed by Princi Singh
 

输出：

The length of the direct common tangent is 2.23607

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