What is the ratio of the incircle area and circumcircle area of a square?
Side of the Square is L.
So, radius of the incircle r = L/2.
The radius of the circumcirlce R = Sq. root of (r^2 + r^2) = Sq. root of (2) * r
=> R^2 = 2 * r^2
The area of the incircle a = Pi * r * r
The area of the circumcircle A = Pi * R * R = Pi * 2 * r^2 = 2 * Pi * r * r = 2 * a
The Ratio of the area of incircle to the circumcirclr = a / (2 *a) = 1 / 2 => 1:2