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 = 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 Sqaure.
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; } |
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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 |
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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 = 6print(ReuleauxArea(r)) # This code is contributed by # Mohit kumar 29 |
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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.. |
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PHP
Output:
50.7434
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