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.

• 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) }
• 8 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)
• 8 years agoHelpfull: Yes(3) No(0)
• 1212r is equal to diagonal of square
  so the ratio of side to radius is 60/7
• 8 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
• 8 years agoHelpfull: Yes(1) No(1)
• sqrt(2)*a=6*r
  hence, a/r = 3/7
• 8 years agoHelpfull: Yes(0) No(2)