A circle circumscribes three unit circles that touch each other. What is the area of the larger circle? Note that p is the ratio of the circumference to the diameter of a circle ( 3.14159265).  Select the correct option:  A) 3.14×(7+43–√3/9)  B) 3.14×(7+43–√3/7)  C) 3.14×(7+43–√3/6)  D) 3.14×(7+43–√3/3)  E) 3.14×(7+43–√3/1)
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–√3/3)   Answer:3.14×(7+43–√3/3)
<result>D</result>
A circle circumscribes three unit circles that touch each other. What is the area of the larger circle? Note that p is the ratio of the circumference to the diameter of a circle ( 3.14159265).