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. Find the ratio of the radius of the circles to the side of the square.
1) [2+ 7sqrt(2)]:1
2) 1:[2+ 6sqrt(2)]
3) 1:[2+ 7sqrt(2)]
4) 1:(4+ 7sqrt(3)]

• Let the radius of circle be r
  let the side of square be a
  then diagonal of square= a*sqrt(2)
  This diagonal length = 12*r + 2r * sqrt(2)
  (because the extreme circle's radius is perpendicular to side of square.)
  Thus we get
  
  12*r+2r*sqrt(2)=a*sqrt(2)
  
  r(6*sqrt(2)+2)=a
  
  r/a=1/(6*sqrt(2)+2)
  
  Thus ratio: r:a = 1:(6*sqrt(2)+2)
  
  Ans: 1:(6*sqrt(2)+2)
• 13 years agoHelpfull: Yes(39) No(5)
• 1/2+6sqrt(2)
• 13 years agoHelpfull: Yes(4) No(5)
• can u explain with diagram,the solution is copy paste of tcs solution,so i am unable to understand.
• 5 years agoHelpfull: Yes(0) No(0)