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 (python):
# Python3 Program to find the biggest Reuleaux 
# triangle inscribed within in a square
# which in turn is inscribed within an ellipse 
import math;

# Function to find the biggest 
# reuleaux triangle 
def Area(a, b):

    # length of the axes cannot 
    # be negative 
    if (a < 0 and b < 0): 
        return -1; 

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

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

    return A; 

# Driver code 
a = 5;
b = 4; 
print(round(Area(a, b), 7));