A circle circumscribes three unit circles that touch each other. What is the area of the larger circle? Note that is the ratio of the circumference to the diameter of a circle ( 3.14159265).

• the ans will be 3.14(1+(2/root(3)))^2. since by joining radius of 3 small circle we will get an equilateral triangle of length 2 unit. and center of the equilateral triangle will be the center of the big circle. so radius of the big circle will be 1+mid point of the equilateral triangle which can be found through the properties of equilateral triangle to be 1/root(3). it can be better visualized with the help of figure only.
• 11 years agoHelpfull: Yes(28) No(3)
• what are the options
  my ans is
  3.14159265*(7 + 4* 3^(1/2))/3
• 11 years agoHelpfull: Yes(9) No(2)
• please explain properly.....
• 11 years agoHelpfull: Yes(6) No(1)
• the ans will be 3.14(1+(1/root(3)))^2. since by joining radius of 3 small circle we will get an equilateral triangle of length 2 unit. and center of the equilateral triangle will be the center of the big circle. so radius of the big circle will be 1+mid point of the equilateral triangle which can be found through the properties of equilateral triangle to be 1/root(3). it can be better visualized with the help of figure only.
• 11 years agoHelpfull: Yes(5) No(2)
• property is center of equilateral triangle that is centroid is center of circle length of line joing vertex of triangle to centroid is 2/3*(root(3)/2*length of side) so here it will be 1/root(3) and adding 1 to it will give you radius of larger circle =1+1/root(3) taking this radius find area of triangle
• 11 years agoHelpfull: Yes(3) No(3)
• my answer is pi(4+2sqrt3)/sqrt3
• 10 years agoHelpfull: Yes(3) No(1)
• there r 3 circles of radius= 1
  if we join there centers we got an equilateral triangle
  the center of the larger circle is the center of this triangle.
• 11 years agoHelpfull: Yes(2) No(7)
• lengthof median of equilateral triangle joining the centers of three circles+radius(which is unity in this case)of small circle= raius of larger circle and thus answer= 15.9sq units
• 11 years agoHelpfull: Yes(1) No(3)
• 
  By joining centers of 3 unit circles we will get an equilateral triangle of length 2 unit. We have to find the length of the orange line.
  And center of the equilateral triangle will be the center of the big circle.
  So radius of the big circle will be = (1 + Circum radius of the equilateral triagle)
  Formula for Circul radius of the equilateral triangle = 23×(3√2a) here 3√2a is the height of the triangle. a is the side of the triangle
  Circum radius of equilateral triangle = 23×3√2×2=23√
  Area of big circle will be =πr2=3.14×(1+23√)2 = 3.14×(1+43√+43)
  =3.14×(1+43√+43) = 3.14×(73+43√)
  =3.14×(7+43√3)
• 9 years agoHelpfull: Yes(1) No(2)
• By joining three unit circles,we get equilateral triangle of 2units length.
  
  As we should find the outer circle joining three circles the center will be center of triangle so radius = (circum radius of equilateral triangle + radius of circle)
  
  R=1+2/√ 3
  
  area= ∏r^2
  
  =∏(1+2/√ 3)^2
  
  =∏/3(2+√ 3)^2
  
• 9 years agoHelpfull: Yes(1) No(1)
• ur ans is wright ANCHAL pls can u explain how it is? i dont know the solution
• 11 years agoHelpfull: Yes(0) No(1)
• i didnot understand this
• 11 years agoHelpfull: Yes(0) No(1)
• 14.9 is the ans
• 11 years agoHelpfull: Yes(0) No(2)
• please explain properly.
• 9 years agoHelpfull: Yes(0) No(1)
• ans=2.154
  source1- http://gogeometry.com/geometry/soddy_descartes_circles.htm
  source2- http://www.geometryexpressions.com/explore.php?p=04-Examples%2F02-Example_Book%2F04-Circles&f=Example_085_Circle_Tangent_To_3_Circles_With_The_Same_Radii.htm
• 9 years agoHelpfull: Yes(0) No(1)
• anyone plz explain clearly...
• 9 years agoHelpfull: Yes(0) No(0)
• By joining centers of 3 unit circles we will get an equilateral triangle of length 2 unit. We have to find the length of the orange line.
  And center of the equilateral triangle will be the center of the big circle.
  So radius of the big circle will be = (1 + Circum radius of the equilateral triagle)
  Formula for Circul radius of the equilateral triangle = 23×(3–√2a)23×(32a) here 3–√2a32a is the height of the triangle. a is the side of the triangle
  Circum radius of equilateral triangle = 23×3–√2×2=23–√23×32×2=23
  Area of big circle will be =πr2=3.14×(1+23–√)2πr2=3.14×(1+23)2 = 3.14×(1+43–√+43)3.14×(1+43+43)
  =3.14×(1+43–√+43)=3.14×(1+43+43) = 3.14×(73+43–√)3.14×(73+43)
  =3.14×(7+43–√3)
• 8 years agoHelpfull: Yes(0) No(0)