Side of a regular n-sided polygon circumscribed in a circle

Given two integers r and n where n is the number of sides of a regular polygon and r is the radius of the circle this polygon is circumscribed in. The task is to find the length of the side of polygon. Examples:

Input: n = 5, r = 11
Output: 12.9256

Input: n = 3, r = 5
Output: 8.6576

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

Approach: Consider the image above and let angle AOB be theta then theta = 360 / n.
In right angled triangle , angle ACO = 90 degrees and angle AOC = theta / 2.
So, AC = OA * sin(theta / 2) = r * sin(theta / 2)
Therefore, side of the polygon, AB = 2 * AC i.e. 2 * r * sin(theta / 2).

Below is the implementation of the above approach:

C++

 // C++ implementation of the approach #include using namespace std;    // Function to calculate the side of the polygon // circumscribed in a circle float calculateSide(float n, float r) {     float theta, theta_in_radians;        theta = 360 / n;     theta_in_radians = theta * 3.14 / 180;        return 2 * r * sin(theta_in_radians / 2); }    // Driver Code int main() {        // Total sides of the polygon     float n = 3;        // Radius of the circumscribing circle     float r = 5;        cout << calculateSide(n, r); }

Java

 // Java  implementation of the approach import java.lang.Math; import java.io.*;    class GFG {        // Function to calculate the side of the polygon // circumscribed in a circle static double calculateSide(double  n, double r) {     double theta, theta_in_radians;        theta = 360 / n;     theta_in_radians = theta * 3.14 / 180;        return 2 * r * Math.sin(theta_in_radians / 2); }    // Driver Code     public static void main (String[] args) {        // Total sides of the polygon     double n = 3;        // Radius of the circumscribing circle     double r = 5;     System.out.println (calculateSide(n, r));     } //This code is contributed by akt_mit     }

Python3

 # Python 3 implementation of the approach from math import sin    # Function to calculate the side of  # the polygon circumscribed in a circle def calculateSide(n, r):     theta = 360 / n     theta_in_radians = theta * 3.14 / 180        return 2 * r * sin(theta_in_radians / 2)    # Driver Code if __name__ == '__main__':            # Total sides of the polygon     n = 3        # Radius of the circumscribing circle     r = 5        print('{0:.5}'.format(calculateSide(n, r)))    # This code is contributed by # Sanjit_Prasad

C#

 // C# implementation of the approach     using System;    class GFG {                 // Function to calculate the side of the polygon      // circumscribed in a circle      static double calculateSide(double n, double r)      {          double theta, theta_in_radians;                 theta = 360 / n;          theta_in_radians = theta * 3.14 / 180;                 return Math.Round(2 * r * Math.Sin(theta_in_radians / 2),4);      }             // Driver Code      public static void Main () {         // Total sides of the polygon      double n = 3;         // Radius of the circumscribing circle      double r = 5;             Console.WriteLine(calculateSide(n, r));      }      // This code is contributed by Ryuga }

PHP



Output:

8.6576

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.