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Anoop managed to draw 6 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 r atio of the side of the square to the radius of the circles. Assume √2 is 1.4.
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- The extreme circles will have radius perpendicular to sides..so the part of diagonal till the centre of cirlce will be sqrt(2)r [Make diagram and it will be clear]..now remaining portion is r , 5 more circles will contribute 10r and last circle will contribute sqrt(2)r + r.
total 12r + 2sqrt(2)r = sqrt(2) side
so ratio of r:s = 1:{2+6sqrt(2) } - 9 years agoHelpfull: Yes(10) No(5)
- distance between centre of the circle and the the adjacent vertex is sqrt(2)*r
so the length of diagonal will be d=10r+ 2*sqrt(2)*r
so the length of a side is d/sqrt(2)
so the ratio is 10+2*sqrt(2)*r : sqrt(2) = 64:7 (ans) - 9 years agoHelpfull: Yes(3) No(0)
- 1212r is equal to diagonal of square
so the ratio of side to radius is 60/7 - 9 years agoHelpfull: Yes(2) No(1)
- 12r=side*sqrt(2)
12r=1.4*s
r=1.4s/12
ratio=s*12/1.4*s=60/7 - 9 years agoHelpfull: Yes(1) No(1)
- sqrt(2)*a=6*r
hence, a/r = 3/7 - 9 years agoHelpfull: Yes(0) No(2)
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