# Biggest Reuleaux Triangle within a Square which is inscribed within a Circle

Given here is a circle of radius r, which inscribes a square which in turn inscribes a reuleaux triangle. The task is to find the maximum possible area of this reuleaux triangle.

Examples:

```Input: r = 6
Output: 50.7434

Input: r = 11
Output: 170.554
```

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

Approach: From the figure, it is very clear that, if the side of the square is a, then

a√2 = 2r
a = √2r

Also, in reuleaux triangle, h = a = √2r, please refer Biggest Reuleaux Triangle within A Sqaure.
So, Area of the Reuleaux Triangle is, A = 0.70477*h^2 = 0.70477*2*r^2

## C++

 `// C++ Program to find the biggest Reuleaux ` `// triangle inscribed within in a square which ` `// in turn is inscribed within a circle ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the Area ` `// of the Reuleaux triangle ` `float` `ReuleauxArea(``float` `r) ` `{ ` ` `  `    ``// radius cannot be negative ` `    ``if` `(r < 0) ` `        ``return` `-1; ` ` `  `    ``// Area of the Reuleaux triangle ` `    ``float` `A = 0.70477 * 2 * ``pow``(r, 2); ` ` `  `    ``return` `A; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``float` `r = 6; ` `    ``cout << ReuleauxArea(r) << endl; ` `    ``return` `0; ` `} `

## Java

 `// Java Program to find the biggest Reuleaux ` `// triangle inscribed within in a square which ` `// in turn is inscribed within a circle ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to find the Area ` `// of the Reuleaux triangle ` `static` `double` `ReuleauxArea(``double` `r) ` `{ ` ` `  `    ``// radius cannot be negative ` `    ``if` `(r < ``0``) ` `        ``return` `-``1``; ` ` `  `    ``// Area of the Reuleaux triangle ` `    ``double` `A = ``0.70477` `* ``2` `* Math.pow(r, ``2``); ` ` `  `    ``return` `A; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``double` `r = ``6``; ` `    ``System.out.println(ReuleauxArea(r)); ` `     `  `} ` `} ` `// This code is contributed by ` `// Surendra_Gangwar `

## Python3

 `# Python3 Program to find the biggest  ` `# Reuleaux triangle inscribed within  ` `# in a square which in turn is inscribed ` `# within a circle ` `import` `math as mt ` ` `  `# Function to find the Area ` `# of the Reuleaux triangle ` `def` `ReuleauxArea(r): ` ` `  `    ``# radius cannot be negative ` `    ``if` `(r < ``0``): ` `        ``return` `-``1` ` `  `    ``# Area of the Reuleaux triangle ` `    ``A ``=` `0.70477` `*` `2` `*` `pow``(r, ``2``) ` ` `  `    ``return` `A ` ` `  `# Driver code ` `r ``=` `6` `print``(ReuleauxArea(r)) ` ` `  `# This code is contributed by  ` `# Mohit kumar 29 `

## C#

 `// C# Program to find the biggest Reuleaux ` `// triangle inscribed within in a square which ` `// in turn is inscribed within a circle ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to find the Area ` `// of the Reuleaux triangle ` `static` `double` `ReuleauxArea(``double` `r) ` `{ ` ` `  `    ``// radius cannot be negative ` `    ``if` `(r < 0) ` `        ``return` `-1; ` ` `  `    ``// Area of the Reuleaux triangle ` `    ``double` `A = 0.70477 * 2 * Math.Pow(r, 2); ` ` `  `    ``return` `A; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main() ` `{ ` `    ``double` `r = 6; ` `    ``Console.WriteLine(ReuleauxArea(r)); ` `} ` `} ` ` `  `// This code is contributed by ` `// shs.. `

## PHP

Output:

```50.7434
```

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