Skip to content
Related Articles

Related Articles

Improve Article

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

  • Last Updated : 17 Mar, 2021

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 <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

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.




My Personal Notes arrow_drop_up
Recommended Articles
Page :