A regular hexagon is inscirbed in a circle of radius R . Another circle is inscribed in the hexagon . Now another hexagon is inscribed in the second ( smaller ) circle .

If thre are some more circle and hexagons inscribed in the similar way as given above, then the ratio of each side of outermost hexagon ( largest one ) to that of the fourth ( smaller cone ) hexagon is ( fourth hexagon means the hexagon which is inside the third hexagon from the outside ):

Options

A. `9 : 3sqrt2`
B. 0.67291666666667
C. `8 : 3sqrt3`
D. none of these

Answer

C