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What would be the ratio of the radius of the circles to the side of the square?
Anoop managed to draw 7 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles on either side.

What would be the ratio of the radius of the circles to the side of the square?<br/>
Anoop managed to draw 7 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles on either side.

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A. 1:(2+ 6√2)
B. 1:(4+ 7√3)
C. (2+ 7√2):1
D. 1:(2+ 7√2)

This question is part of @TCS-mock test
Asked by Mr.venkat, Last updated: Apr 02, 2020

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John Smith

John Smith

Answered Sep 30, 2016

1:(2+ 6√2)

The extreme circles will have radius perpendicular to sides of square so the part of diagonal till the centre of circle will be sqrt(2) r and remaining portion is r , 5 more circles will contribute 10r and last circle will contribute r + sqrt(2) r . Length of diagonal = 12r + 2sqrt (2) r = sqrt (2) s where s -> side of square. So, ratio of r:s = 1/( 2 + 6 sqrt(2)) = 1: [ 2+ 6 sqrt(2)]
 

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