In the adjoining figure ABCD is a square . A circle ABCD is passing through all the four vertices of the square. There are two more circles on the sides AD and BC touching each other inside the square , AD and BC are the respective diameters of the two smaller circles. Area of the square is `16 cm^(2)`.

What is the area of region 2 ?

Options

A. `3 ( pi -2) cm^(2) `
B. ` (pi -3 ) cm^(2) `
C. ` (2 pi -3) cm^(2) `
D. ` 4( pi -2) cm^2`

Answer

D