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

Last Updated : 28 Jul, 2022

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```

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 Square
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

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## Javascript

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Output:

`50.7434`

Time Complexity: O(1)

Auxiliary Space: O(1)

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