there is a circle which circumscribes three unit circles which are tangential to each other .What is the circumference of the bigger circle?

a)pi(7+2 *sqrt 3)/sqrt3 b)pi(5+4*sqrt3)/sqrt3
c)pi(5+2*sqrt3)/sqrt3 c)pi(4+2*sqrt3)/sqrt3

• centers of 3 circles form eq triangle of side 2
  
  join center of big circle to any other centre & draw perpendicular
  
  cos 30 = 1 / x => x = 2/ sqrt(3) where, x = distance b/w centres of smaller & bigger circle.
  
  then the radius of the bigger circle r=2/sqrt3+1
  
  and the circumference of the bigger circle=2*pi*r=2*pi*(1+2/sqrt3)=pi(2+4/sqrt3)=pi(4+2*sqrt3)/sqrt3
  
  so d is the correct answer
  
• 9 years agoHelpfull: Yes(15) No(0)
• centres of 3 circles form eq triangle of side 2
  join centre of big circle to any other centre & draw perpendicular
  
  cos 30 = 1 / x => x = 2/ root(3) where, x = distance b/n centres of smaller & bigger circle.
  
  R = (1 + 2/root3) = 2.15
  
  Area of larger circle = 3.14 * (2.15)^2 = 14.57 sq unit
  
• 9 years agoHelpfull: Yes(0) No(6)
• centre of he bigger circle is the incentre of the equilateral tringle formed by matching the radius of inner circle of rasius 1.so sides of equilateral tringle is2.deawing perpendicular bisector from one vertices to the front side and findin the perpendicular length with thw help of pithagorus theorem we get sqrt(3).from ere we find the radius of bigger circle is (2/sqrt(3)+1)
  so circumference is pi(4+2*sqrt3)/sqrt3.
• 9 years agoHelpfull: Yes(0) No(0)
• answer is 191
• 9 years agoHelpfull: Yes(0) No(0)