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 (java):
// Java Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within an ellipse
import java.io.*;

class InfobayAI 
{
    
// Function to find the biggest reuleaux triangle
static 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 = (float)Math.sqrt(((Math.pow(a, 2) + Math.pow(b, 2))
                / (Math.pow(a, 2) * Math.pow(b, 2))));

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

    return A;
}

// Driver code
public static void main (String[] args)
{
    float a = 5, b = 4;
    System.out.println(Area(a, b));
}
}