Latest TCS Aptitude Question SOLUTION: 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 t

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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

Solution

Draw an square, and make 7 circles in the diagonal in such a way that two corner circles could touch the two sides of the square.
Let the length of the side of the square and radius of the circle are respectively a and r. Then diagonal of the square = a(sqrt2)
since this diagonal contains 7 circles and a bit extra length in both the corners so relation will be
a(sqrt2) = r(sqrt2) + r + 2r*5 + r + r(sqrt2)
or a(sqrt2) = 2r(sqrt2) + 12r
or r/a = (sqrt2)/[2(sqrt2) + 12]
or r/a = 1/[2 + 6(sqrt2)]

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Asked In TCS bristi (13 years ago)

Solved Read Solution (3)

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Read Solution (3) :

suchandra raavi  (13 years ago)

First refer to the diagram in the following link:
http://writer.zoho.com/public/suchandra/ques
1)In the diagram let the radius of each circle be "x"
2)Now the arrangement forms two small squares at the end of the diagonal on both sides as shown. Since radius of circle is x, we can calculate the diagonal length at these ends which is x√2. Both sides, so total of 2√2x.
3)Now the remaining length of the diagonal is easy. It is 12x.
4)Total length of the diagonal is now 2√2x + 12x
5)we can now get the length of the side of a square =(2√2x + 12x)/√2 = 2x+6√2x -->(side = diagonal/âˆ

Is this solution Helpfull? Yes (15) | No   

SUBHAJIT GUHA  (13 years ago)

First refer to the diagram in the following link:
http://writer.zoho.com/public/suchandra/ques

At first let the side of the square is x
then the length of the diagonal is sqrt of 2 *x.

In the diagram length of the diagonal created by 7 circle r 12r where r is the radius of the circles.
So ratio will be r/x=sqrt of 2/12r.
ans will be C

Is this solution Helpfull? Yes (3) | No (1)  

Shreya  (13 years ago)

yes. 3rd option is correct 1:(2+6root2)

Is this solution Helpfull? Yes (1) | No (1)  

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