圆心相距D的两个圆的交角

给定两个正整数R1和R2，代表两个相交圆的半径，它们的中心之间的距离为D ，任务是找到两个圆之间相交角的余弦。

例子：

Input: R1 = 3, R2 = 4, D = 5
Output: 0

Input: R1 = 7, R2 = 3, D = 6
Output: 0.52381

方法：给定的问题可以通过使用几何算法来解决，如下图所示：

From the above image and using the Pythagoras Theorem, the cosine of the angle of intersection of the two circles can be found using the formula:

$cos \theta = \frac{R1^2 + R2^2 - D^2}{2 * R1 * R2}$

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to find the cosine of the
// angle of the intersection of two
// circles with radius R1 and R2
float angle(float R1, float R2, float D)
{
    float ans = (R1 * R1 + R2 * R2 - D * D)
                / (2 * R1 * R2);
 
    // Return the cosine of the angle
    return ans;
}
 
// Driver Code
int main()
{
    float R1 = 3, R2 = 4;
    float D = 5;
    cout << angle(R1, R2, D);
 
    return 0;
}

Java

// Java program for the above approach
import java.io.*;
 
class GFG{
     
// Function to find the cosine of the
// angle of the intersection of two
// circles with radius R1 and R2
static float angle(float R1, float R2, float D)
{
    float ans = (R1 * R1 + R2 * R2 - D * D) /
               (2 * R1 * R2);
                
    // Return the cosine of the angle
    return ans;
}
 
// Driver Code
public static void main (String[] args)
{
    float R1 = 3, R2 = 4;
    float D = 5;
     
    System.out.println(angle(R1, R2, D));
}
}
 
// This code is contributed by Ankita saini

Python3

# Python3 program for the above approach
 
# Function to find the cosine of the
# angle of the intersection of two
# circles with radius R1 and R2
def angle(R1, R2, D):
     
    ans = ((R1 * R1 + R2 * R2 - D * D) /
            (2 * R1 * R2))
 
    # Return the cosine of the angle
    return ans
 
# Driver Code
if __name__ == '__main__':
     
    R1 = 3
    R2 = 4
    D = 5
     
    print(angle(R1, R2, D))
     
# This code is contributed by ipg2016107

C#

// C# program for the above approach
using System;
 
class GFG{
     
// Function to find the cosine of the
// angle of the intersection of two
// circles with radius R1 and R2
static float angle(float R1, float R2, float D)
{
    float ans = (R1 * R1 + R2 * R2 - D * D) /
               (2 * R1 * R2);
                
    // Return the cosine of the angle
    return ans;
}
 
// Driver Code
public static void Main(string[] args)
{
    float R1 = 3, R2 = 4;
    float D = 5;
     
    Console.Write(angle(R1, R2, D));
}
}
 
// This code is contributed by rutvik_56.

Javascript

 
// Javascript program for the above approach 
 
// Function to find the cosine of the
// angle of the intersection of two
// circles with radius R1 and R2
function angle(R1, R2, D)
{
    var ans = (R1 * R1 + R2 * R2 - D * D) /
               (2 * R1 * R2);
 
    // Return the cosine of the angle
    return ans;
}
 
// Driver Code
var R1 = 3, R2 = 4;
var D = 5;
 
document.write(angle(R1, R2, D));
 
// This code is contributed by Ankita saini
 

输出：

0

时间复杂度： O(1)
辅助空间： O(1)

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