A square is inscribed in a circle then another circle is inscribed in the square . Another square is then inscribed in the circle. Finally a circle is inscirbed in the innermost square . Thus there are 3 circles and 2 squares as shown in the figure . The radius of the outer - most circle is R .

What is the ratio of sum of circumference of all the circles to the sum of perimeters of all the squares ?

Options

A. `(2 + sqrt(3))pi R `
B. `(3 + sqrt(2)) pi R `
C. `3 sqrt(3) pi R `
D. none of these

Answer

D