Program to find the Circumcircle of any regular polygon

Given a n-sided polygon with side length a. The task is to find the area of the cicumcircle of the polygon.

Examples:

Input: n = 10, a = 3
Output: 1.99737

Input: n = 5, a = 6
Output: 3.02487


Approach: A regular n-gon divides the circle into n pieces, so the central angle of the triangle is a full circle divided by n: 360 deg/n.
Applying the law of cosines for the three side lengths of the triangle, we get

c2 = a2 + b2 – 2ab cos C
or, a2 = r2 + r2 – 2rr cos (360/n)
or, a2 = 2r2 – 2r2 cos (360/n)
or, c2 = r2 (2 – 2 cos (360/n))
so, a=r√(2-2cos(360/n))

Therefore,
r=a/√(2-2cos(360/n))

Below is the implementation of the above approach:

C++

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// C++ Program to find the radius
// of the circumcircle of the given polygon
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the radius
// of the circumcircle
float findRadiusOfcircumcircle(float n, float a)
{
  
    // these cannot be negative
    if (n < 0 || a < 0)
        return -1;
  
    // Radius of the circumcircle
    float radius = a / sqrt(2 - (2 * cos(360 / n)));
  
    // Return the radius
    return radius;
}
  
// Driver code
int main()
{
  
    float n = 5, a = 6;
  
    // Find the radius of the circumcircle
    cout << findRadiusOfcircumcircle(n, a) << endl;
  
    return 0;
}

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Java

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// Java Program to find the radius
// of the circumcircle of the given polygon
  
import java.io.*;
  
class GFG {
    
// Function to find the radius
// of the circumcircle
static float findRadiusOfcircumcircle(float n, float a)
{
  
    // these cannot be negative
    if (n < 0 || a < 0)
        return -1;
  
    // Radius of the circumcircle
    float radius = (float)(a / Math.sqrt(2 - (2 * Math.cos(360 / n))));
  
    // Return the radius
    return radius;
}
  
// Driver code
  
    public static void main (String[] args) {
        float n = 5, a = 6;
  
    // Find the radius of the circumcircle
    System.out.println( findRadiusOfcircumcircle(n, a)) ;
  
    }
}
// This code is contributed 
// by anuj_67..

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Python 3

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# Python3 Program to find the 
# radius of the circumcircle 
# of the given polygon 
  
# from math import all methods
from math import *
  
# Function to find the radius 
# of the circumcircle 
def findRadiusOfcircumcircle(n, a) :
  
    # these cannot be negative
    if n < 0 or a < 0 :
        return -1
  
    # Radius of the circumcircle
    radius = a / sqrt(2 - (2 * cos(360 / n)))
  
    # Return the radius
    return radius
  
# Driver code
if __name__ == "__main__" :
  
    n , a = 5, 6
  
    # Find the radius of the circumcircle 
    print(round(findRadiusOfcircumcircle(n, a), 5))
  
# This code is contributed 
# by ANKITRAI1

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C#

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// C# Program to find the radius
// of the circumcircle of the given polygon
using System;
  
class GFG 
{
  
// Function to find the radius
// of the circumcircle
static float findRadiusOfcircumcircle(float n, 
                                      float a)
{
  
    // these cannot be negative
    if (n < 0 || a < 0)
        return -1;
  
    // Radius of the circumcircle
    float radius = (float)(a / Math.Sqrt(2 - 
                   (2 * Math.Cos(360 / n))));
  
    // Return the radius
    return radius;
}
  
// Driver code
public static void Main () 
{
    float n = 5, a = 6;
  
    // Find the radius of the circumcircle
    Console.WriteLine(findRadiusOfcircumcircle(n, a));
}
}
  
// This code is contributed 
// by anuj_67

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PHP

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<?php
// PHP Program to find the radius 
// of the circumcircle of the 
// given polygon 
  
// Function to find the radius 
// of the circumcircle 
function findRadiusOfcircumcircle($n, $a
  
    // these cannot be negative 
    if ($n < 0 || $a < 0) 
        return -1; 
  
    // Radius of the circumcircle 
    $radius = $a / sqrt(2 - (2 * 
                    cos(360 / $n))); 
  
    // Return the radius 
    return $radius
  
// Driver code 
$n = 5;
$a = 6; 
  
// Find the radius of the circumcircle 
echo findRadiusOfcircumcircle($n, $a); 
  
// This code is contributed by Anuj_67..
?>

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Output:

3.02487


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