Latest TCS Aptitude Question SOLUTION: There is a square. 5 circles are kept on the diagonal of the square such that the two extreme circles touch the two sides of the square.each circle has equal radius.find the ratio

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There is a square. 5 circles are kept on the diagonal of the square such that the two extreme circles touch the two sides of the square.each circle has equal radius.find the ratio of side of hte squae to that of the radius.

Asked In TCS RajkumarMahanta (12 years ago)

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suchandra raavi  (12 years ago)

Draw a square, and make 5 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 5 circles and a bit extra length in both the corners so relation will be
a(sqrt2) = r(sqrt2) + r + 2r*3 + r + r(sqrt2)
or a(sqrt2) = 2r(sqrt2) + 8r
or r/a = (sqrt2)/[2(sqrt2) + 8]
or r/a = 1/[2 + 4(sqrt2)]

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Ambika Prasad Tiwari  (12 years ago)

let the length of the each side of square be a and radius of the circle be r
since 5 circles have been placed around the diagonal so
length of diagonal of the square=sum of diameters of all the circles
a*sqrt(2)=10r
so a/r=10/sqrt(2)
a/r=5*sqrt(2)

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suchandra raavi  (12 years ago)

@amitabh, a/r is asked, did not see. Just reverse the equation , its [2 + 4(sqrt2)]:1

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Rimu Mukherjee  (12 years ago)

7.6:1
8r+2sqrt2r=sqrta

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AMITABH BARMAN  (12 years ago)

@suchandra ravi,ur solution is perfectly alright but tell me will it be a/r or r/a???

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Harsh Gupta  (12 years ago)

On diagonal 5 circle..and two circle touch two side of square.their diameter will be r(sqrt2)+r.And diameter of circle which is on the diagonal is 2r.
length of diagonal is a(sqrt2)
a(sqrt)=2(r(sqrt(2)+r)+3*2r
r/a=1/[2+4(sqrt(2)]

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