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

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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

Approach: Consider the image above and let angle AOB be theta then theta = 360 / n.
In right angled triangle $\Delta AOC$ , 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 <bits/stdc++.h>
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

<?php
// PHP implementation of the approach
 
// Function to calculate the side of the 
// polygon circumscribed in a circle
function calculateSide($n, $r)
{
    $theta; $theta_in_radians;
 
    $theta = 360 / $n;
    $theta_in_radians = $theta * 3.14 / 180;
 
    return 2 * $r * sin($theta_in_radians / 2);
}
 
// Driver Code
 
// Total sides of the polygon
$n = 3;
 
// Radius of the circumscribing circle
$r = 5;
 
echo calculateSide($n, $r);
 
// This code is contributed by inder_verma..
?>

Javascript

<script>
 
// javascript  implementation of the approach
 
    
// Function to calculate the side of the polygon
// circumscribed in a circle
function calculateSide( n , r)
{
    var 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
 
// Total sides of the polygon
var n = 3;
 
// Radius of the circumscribing circle
var r = 5;
document.write(calculateSide(n, r).toFixed(5));
 
// This code contributed by Princi Singh 
 
</script>

Output

8.6576

Time Complexity: O(1), since there is no loop or recursion.
Auxiliary Space: O(1), since no extra space has been taken.

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