Given two positive integers R1 and R2 representing the radius of two intersecting circles having a distance D between their centers, the task is to find the cosine of the angle of intersection between the two circles.
Examples:
Input: R1 = 3, R2 = 4, D = 5
Output: 0Input: R1 = 7, R2 = 3, D = 6
Output: 0.52381
Approach: The given problem can be solved by using the Geometric Algorithm as illustrated below:
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:
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to find the cosine of the// angle of the intersection of two// circles with radius R1 and R2float 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 Codeint 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 R2static 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 Codepublic 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 R2def angle(R1, R2, D): ans = ((R1 * R1 + R2 * R2 - D * D) / (2 * R1 * R2)) # Return the cosine of the angle return ans# Driver Codeif __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 R2static 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 Codepublic 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
<script>// Javascript program for the above approach // Function to find the cosine of the// angle of the intersection of two// circles with radius R1 and R2function angle(R1, R2, D){ var ans = (R1 * R1 + R2 * R2 - D * D) / (2 * R1 * R2); // Return the cosine of the angle return ans;}// Driver Codevar R1 = 3, R2 = 4;var D = 5;document.write(angle(R1, R2, D));// This code is contributed by Ankita saini</script> |
Output:
0
Time Complexity: O(1)
Auxiliary Space: O(1)
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