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

Recommended: Please try your approach on {IDE} first, before moving on to the solution. 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++

 // C++ Program to find the radius // of the circumcircle of the given polygon    #include 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; }

Java

 // 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..

Python 3

 # 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

C#

 // 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

PHP



Output:

3.02487

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Improved By : vt_m, AnkitRai01

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