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++ 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 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 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 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# 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. |
<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 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 </script> |
Output:
0
Time Complexity: O(1)
Auxiliary Space: O(1)