A circle of radius ‘r’ is inscribed in a square. The mid points of sides of square are joined to form a new square. The mid point of sides of resulting square are again joined so that a new square was obtained and so on. Then radius of circle inscribed in nth square is

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$[2^{\frac{n - 1}{2}}] r$

$[2^{- \frac{n}{2}}] r$

$[2^{\frac{1 - n}{2}}] r$

$[2^{\frac{3 - 3 n}{2}}] r$

answer is A.

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Detailed Solution

Clearly radius of 2nd circle $= \frac{\sqrt{r^{2} + r^{2}}}{2} = \frac{r}{\sqrt{2}}$
and third circle $= \frac{r}{2}$
radius of nth circle $= \frac{r}{2^{[\frac{n - 1}{2}]}}$

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