Question

Anoop managed to draw 5 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.Find the ratio of the the side of the square to radius of the circles. You may assume that square root of 2 is 1.4

A. 2.2
B. 3
C. 8.9
D. 7.6

Explanation

Let the radius of circle be r
let the side of square be a
then diagonal of square= a*sqrt(2)
This diagonal length = 8*r + 2r * sqrt(2)
(because the extreme circle's radius is perpendicular to side of square.)
Thus we get

8*r+2r*sqrt(2)=a*sqrt(2)

r(4*sqrt(2)+2)=a
so a/r=(4*sqrt(2)+2)/1
Thus ratio: a:r =(4*sqrt(2)+2)/1
= 7.6
Ans: 7.6


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