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 cirle touches tow cirles on either side. Find the ratio of the side of square to radius of the circle . You may assume that square root of 2 is 1.4

10.40:1
13.90:1
11.80:1
15.90:1

• first make a circle of side=a
  now draw 7 circle on diagonal of the square keep in mind last two circle on the diagonal touch the square side---
  now u see that last two circle on the end of the diagonal not touches the corner of the diagonal- i try to make such figure so u see some space left at the corner of the diagonal-
  _________
  |O |
  | O |
  | O |
  | O |
  | O |
  | O |
  |______O|
  diagonal=14r+2(space left on the corner)
  as it given its make square on the last circle so diagonal of that circle=root2r
  so now diagonal= 12r+2r root2
  diagonal=a root2
  a root2=12r +2r root2
  a/r=12+2 root2/root2=2+6 root2/1=10.4/1
• 13 years agoHelpfull: Yes(5) No(1)
• consider a diagonal of a circle.
  as it s given as 7 circles..assume dat u hv drawn 7 circles on the diagonal.
  now its lik the ratio of side of square:radius of a circle
  dats, d/root(2):1
  now, substitute for d/root(2) ur given ques and find out the answer..
• 13 years agoHelpfull: Yes(3) No(3)
• 7 circles are drawn on the diagonal of the square,,, making the legth of the diagonal 14r. and we know that the diagonal of a square is root2 * a . therefore.. root 2 * a = 14r therefore a/r= 14/ root2
• 13 years agoHelpfull: Yes(2) No(3)
• ans is 10.4:1......the formula is (x-1)2*2+2:1
• 13 years agoHelpfull: Yes(1) No(1)
• let square of side A, and radius of each circle is R.
  after sketching 7 circles according to question, we see that some gap b/w corner of square and extreme circles,thus calculating for that space:
  meet the centre of extreme circle to point,which touching square on both side of square. which will form a small square of side R, hence diagonal will be root2*R, and gap outside will be (diagonal - radii of circle) which mean root2*R - R,
  which will be same for another extreme circle.
  hence diagonal of big square = 7 * 2R + 2(root2*R - R) = 14.8 R.
  Hence side of square =diagonal/root2 = 10.57 R
  hence ratio will be 10.57 : 1.
  which is close to ans(A).
• 13 years agoHelpfull: Yes(1) No(0)
• Let the radius of the circle be 'r' and the side of the square be 'a'.Then, the length of the diagonal of the square is square root (2) * a. Since, the diagonal has 7 circles of equal radii, then, the diagonal of the square equals 14r.So, 14r=sqrt(2)*a, So, a/r=14/sqrt(2). Since, sqrt(2)=1.4(approximately), the ratio is 10.40:1. With regards,GBA.
• 12 years agoHelpfull: Yes(1) No(1)
• please poornima while submitting ur ans please explain them
  its difficult to understand from formula
  what logic is behind the problem
• 13 years agoHelpfull: Yes(0) No(1)
• i am sorry ankit..i couldnt explain u more accurate via dis..
• 13 years agoHelpfull: Yes(0) No(1)
• its right Nandita
  But how u r matching the ans with the option given in Q
  
• 13 years agoHelpfull: Yes(0) No(1)
• ansssss is 10.40:1.......pls explain the procedure how to solve the problem.......tell us the method
• 13 years agoHelpfull: Yes(0) No(1)
• hai frnd i will try some wht to axplain clerlr but one thing ans is option -1....
  coming to solotion......he had drawn 7 circles on diagonal...means we will have total 7 diameters and small portin will left at the corner if u cant understan draw on paper u will clearly visualise a small portion of diagonal is missing.... now 7 diameters and that sum we have to calclulate.....as it given last two circles at edges are touching the sides so there uin last two circles draw perpendiculars on to the side which gives u a squre with side equal to circles radius....from that calculate the digonal of the square.... we can use simple phytogorus principle to get those values... then at last we had left with
  12 radius + 2 times the diagonla of square formed due to radius r.... now eualise total diagonal of the big square to the summ of lengths in terms of r we will get 2+6sqrt(2):1 ..... on simplification gives 10.40:1...... any douts catch me at pavan_gvs@yahoo.com......
• 13 years agoHelpfull: Yes(0) No(2)
• Let side of square = a and radius of circle = r
  7 circles = 5 middle circles + 2 end circles
  so length of diagonal = 5x2r + 2xr = 12r
  also length of diagonal = a x sqrt(2) = 1.4a
  hence 12r = 1.4a or a/r = 12/1.4 = 8.57
  none of the options is right
  
• 13 years agoHelpfull: Yes(0) No(1)
• its 19.6:1.....
  n plz use correct spellings....its getting much confused...
• 12 years agoHelpfull: Yes(0) No(1)