两个不相交圆之间的直接公共切线的长度

原文:https://www . geeksforgeeks . org/两个不相交圆之间的直交切线长度/

给定半径的两个圆，它们的圆心相距给定的距离，这样两个圆就不会相互接触。任务是找到圆之间的直接公共切线的长度。 例:

Input: r1 = 4, r2 = 6, d = 12 
Output: 11.8322

Input: r1 = 5, r2 = 9, d = 25
Output: 24.6779

接近 :

  • 让圆的半径分别为 r1 & r2 。
  • 让中心之间的距离为 d 单位。
  • 画一条线或平行于 PQ
  • 角度 OPQ = 90 度 角度奥 QP = 90 度
  • 角度 OPQ +角度 O'QP = 180 度 OP || QR
  • 由于对边平行，内角为 90°，因此 OPQR 为矩形。
  • 所以 OP = QR = r1 和 PQ = OR = d
  • 在三角形中oo’r angle oro’= 90 由勾股定理 or^2+o'r^2 =(oo'^2) or^2+(r1-r2)^2 = d^2
  • 所以，or^2= d^2-(r1-r2)^2T2或= √{d^2-(r1-r2)^2}t5length of direct common tangent = sqrt((distance between centers)^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 donot 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, 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 = 12;
    lengtang(r1, r2, d);
    return 0;
}

Java 语言(一种计算机语言，尤用于创建网站)

// Java program to find
// the length of the direct
// common tangent between two circles
// which donot touch 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 = 12;
    lengtang(r1, r2, d);
}
}

/* This code contributed by PrinciRaj1992 */

Python 3

# Python3 program to find
# the length of the direct
# common tangent between two circles
# which do not touch each other
import math

# 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 = 12;
lengtang(r1, r2, d);

# This code is contributed by 29AjayKumar

C

// C# program to find
// the length of the direct
// common tangent between two circles
// which donot touch 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()
    {
        double r1 = 4, r2 = 6, d = 12;
        lengtang(r1, r2, d);
    }
}

// This code is contributed by AnkitRai01

服务器端编程语言（Professional Hypertext Preprocessor 的缩写）

<?php
// PHP program to find the length
// of the direct common tangent
// between two circles which
// donot touch each other

// Function to find the length
// of the direct common tangent
function lengtang($r1, $r2, $d)
{
    echo "The length of the direct",
            " common tangent is ",
        sqrt(pow($d, 2) -
            pow(($r1 - $r2), 2)), "\n";
}

// Driver code
$r1 = 4;
$r2 = 6;
$d = 12;
lengtang($r1, $r2, $d);

// This code is contributed by akt_mit
?>

java 描述语言

<script>

// Javascript program to find
// the length of the direct
// common tangent between two circles
// which donot touch 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)));
}

// Driver code
    var r1 = 4, r2 = 6, d = 12;
    lengtang(r1, r2, d);

</script>

输出:

The length of the direct common tangent is 11.8322

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