Problem: Biggest Reuleaux Triangle inscribed within a square which is inscribed within an ellipse
Given an ellipse with major axis length and minor axis 2a & 2b respectively which inscribes a square which in turn inscribes a reuleaux triangle. The task is to find the maximum possible area of this reuleaux triangle.

Sample Input: a = 5, b = 4
Sample Output: 0.0722389

Solution (cpp):
// C++ Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within an ellipse
#include <bits/stdc++.h>
using namespace std;

// Function to find the biggest reuleaux triangle
float Area(float a, float b)
{

    // length of the axes cannot be negative
    if (a < 0 && b < 0)
        return -1;

    // height of the reuleaux triangle
    float h = sqrt(((pow(a, 2) + pow(b, 2))
                    / (pow(a, 2) * pow(b, 2))));

    // area of the reuleaux triangle
    float A = 0.70477 * pow(h, 2);

    return A;
}

// Driver code
int main()
{
    float a = 5, b = 4;
    cout << Area(a, b) << endl;

    return 0;
}