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
Time Complexity: O(1)
Auxiliary Space: O(1)
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