If three circles are inscribed inside a circle. The radius of the small circles is r. What is the radius of the big circle?

• centres of 3 circles form an eq. triangle of side 2r.
  
  if distance b/n smaller & bigger circle be x
  cos30 = r/x => 2r/√3
  
  Radius of bigger circle = r+x = r + 2r/√3 = r(1+ 2/√3)= 2.155r
• 9 years agoHelpfull: Yes(34) No(4)
• let distane of smaller circle to bigger circle is x.
  so,cos30=r/x
  (3^1/2)/2=r/x
  we get x as 1.15r
  so radius of bigger circle is r+1.15r=2.15r
• 9 years agoHelpfull: Yes(5) No(1)
• radius of big circle is 2r
• 9 years agoHelpfull: Yes(2) No(6)
• if 3 circles are inscribed in a large circle it forms an equilateral triangle.the center of the large circle becomes the point of intersection of medians of three sides of a triangle..As for equilateral triangle all the sides are equal so the median is same for all i.e,. (√3/2)side of triangle.
  therefore (√3/2)2r=√3r
  hence radius of the large circle is √3r+r=(√3+1)r
  =(1.717+1)r
  =2.71r
• 9 years agoHelpfull: Yes(2) No(0)
• max 2r ,,just because if 3 small circle inside the big circle take half of the radious of big circle.
  
• 9 years agoHelpfull: Yes(0) No(0)
• @Ankita: better to marry with your answer.....
• 9 years agoHelpfull: Yes(0) No(0)
• r
  Bcz all circles may be of same radius
• 9 years agoHelpfull: Yes(0) No(2)