# 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 = 6Output:50.7434Input:r = 11Output:170.554

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

aâˆš2 = 2ra = âˆš2r

Also, in reuleaux triangle, **h = a = âˆš2r**, 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 <bits/stdc++.h>` `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

`<?php` `// PHP Program to find the biggest Reuleaux` `// triangle inscribed within in a square` `// which in turn is inscribed within a circle` `// Function to find the Area of the` `// Reuleaux triangle` `function` `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;` `echo` `ReuleauxArea(` `$r` `) . ` `"\n"` `;` `// This code is contributed by ita_c` `?>` |

## Javascript

`<script>` `// javascript Program to find the biggest Reuleaux` `// triangle inscribed within in a square which` `// in turn is inscribed within a circle` `// Function to find the Area` `// of the Reuleaux triangle` `function` `ReuleauxArea(r)` `{` ` ` `// radius cannot be negative` ` ` `if` `(r < 0)` ` ` `return` `-1;` ` ` `// Area of the Reuleaux triangle` ` ` `var` `A = 0.70477 * 2 * Math.pow(r, 2);` ` ` `return` `A;` `}` `// Driver code` `var` `r = 6;` `document.write(ReuleauxArea(r));` `// This code contributed by Princi Singh` `</script>` |

**Output:**

50.7434

**Time Complexity: **O(1)

**Auxiliary Space: **O(1)