question_answer

A circle of radius r is inscribed in a square. The mid-points of sides of the square have been connected by line segment and a new square resulted. The sides of the resulting square were also connected by segment so that a new square was obtained and so on, then the radius of the circle inscribed in the \[{{n}^{th}}\] square is ____.

A)  \[\left[ {{2}^{\frac{1-n}{2}}} \right].r\] 

B)  \[\left[ {{2}^{\frac{3-3n}{2}}} \right].r\]

C)  \[\left[ {{2}^{\frac{-n}{2}}} \right].r\]               

D)  \[\left[ {{2}^{-\,\frac{5-3n}{2}}} \right].r\]

E)  None of these