# 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
```

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