# 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

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

 ``

## Javascript

 ``

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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