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anup managed to draw 7 circle of equal raddi with their centres on the diagonal of a square such that the two extreme circle touch two sides of the square and each middle circle touches two circle on other side.find the ratio of the radious of the circle to the side of the square.

(2+7root 2):1
1:(2+7root 2)
1:(2+6root 2)
1:(4+7root 3)

please explain

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TCS Other Question

planet fourfi resides in 4 dimensional space & thus the currency used by its residents are 3 dimensional objects. The rupee are cubical in shape while their coins are spherical, however the coin minting machinery lays out some stipulations on the size of the coins. The diameter of the coins should be at least 64mm & not exceed 512 mm.
Given a coin,the diameter of the next larger coin is at least 50% greater then the diameter of the previous coin. All the diameters must always be an integer. You are asked to design a set of coins of different diameters with these requirements & your goal is to design as many as coin as possible.how many coins can you design?

a)9 b)5 c)6 d)8

please explain
a hare & a tortoise have a race along a circle of 100 yards diameter.the tortoise goes in 1 direction & hare in another.after the tortoise has covered 1/5th of its distance & that is too leisurely.the hare & tortoise meet when the hare has covered only 1/8 th of the distance.by what factor should the hare increase its speed so as it to tie the race?
5
8
37.80
40

please explain