In an exam, students were asked to find the perimeter of a square which contains three circles such that their enters on the diagonal of the square , the middle circle touches two extreme circles on either side and two extreme circles touch two sides of the square and the radius of the three are equal . And ate what times the radius equals the perimeter?

• Let the radius of circle be r
  let the side of square be a
  then diagonal of square= a*sqrt(2)
  This diagonal length = 4*r + 2r * sqrt(2)
  (because the extreme circle's radius is perpendicular to side of square.)
  Thus we get
  
  4*r+2r*sqrt(2)=a*sqrt(2)
  
  r(2*sqrt(2)+2)=a
  
  r/a=1/(2*sqrt(2)+2)
  
  Thus ratio: r:4a = 1:4(2*sqrt(2)+2)
  
• 11 years agoHelpfull: Yes(20) No(2)
• let side of sqr =a
  perimeter=4*a
  also diagonal=a* sqrt(2)
  as the 3 circles lie on diagonal,so
  6*r=a*sqrt(2)
  substituting a= perimeter/4
  6*r=p*sqrt(2)/4
  12*sqrt(2) r=p
  
• 11 years agoHelpfull: Yes(13) No(11)
• side of square =a
  no of circles=n=3(here)
  radius of each circle=r
  a:r=((n-1)sqrt(2)+2):1
  solving this we get perimeter=(8*sqrt(2)+8)r
  
• 11 years agoHelpfull: Yes(4) No(5)
• 32 times Radius = Parameter of Square.
  COZ, ATQ,
  Parameter = 2(3*Raduis(R) + Remaining part of Diagonal of Square(X)).
  Solve for R=1 and X=1.
  Side of Square (A) = 8 units.
  hence,
  32R = P.
• 11 years agoHelpfull: Yes(2) No(2)
• 12(root2) is ans
• 11 years agoHelpfull: Yes(2) No(3)
• a(sqrt2) = diagonal = r sqrt2 + r + 2r + r + r sqrt2 = 4r + 2r sqrt2
  a = (4r + 2r sqrt2) / sqrt2
  a = 4r/sqrt2 + 2r sqrt2 / sqrt2
  a = (2 x 2r) / sqrt2 + 2r
  
  But we know, 2/sqrt2 = sqrt2. Therefore, above equation becomes,
  Let the radius of circle be r.
  Let the side of the square be a.
  Then Diagonal = a(sqrt2) a = 2r sqrt2 + 2r = 2r(sqrt2+1)
  Then perimeter of the square = 4a = 4 x 2r(sqrt2+1) = 8r(sqrt2+1)
  = 8r(1.414+1) = 8r(2.414) = r(19.312)
  Hence 19.312 time radius equals the perimeter of the square.
• 11 years agoHelpfull: Yes(2) No(0)
• @nikhil
  which is the right ans...?
• 11 years agoHelpfull: Yes(1) No(0)
• (sqrt(2)+1)*8..
  
  side of square=(4r+sqrt(2)r+sqrt(2)r)/sqrt(2)
• 11 years agoHelpfull: Yes(0) No(1)
• see the sol of AMANDEEP SINGH its right
• 11 years agoHelpfull: Yes(0) No(0)
• 2sqrt2(r)+4r=sqrt2 (a)
  a=2r(1+sqrt2)
  p=8r(1+sqrt2)
• 11 years agoHelpfull: Yes(0) No(0)