# 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

 ``

## Javascript

 ``

Output:

`50.7434`

Time Complexity: O(1)

Auxiliary Space: O(1)

My Personal Notes arrow_drop_up