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