Three circles each of radius 3.5 cm touch one another

Three circles each of radius 3.5 cm touch one another. The area subtended between them is

  1. 6(√3π - 2) square units
  2. 6(2π - √3) square units
  3. 49/8 (2√3 - π) square units
  4. 49/8 (√3 - π) square units 8

Answer

Draw equilateral triangle ABC by connecting the centers of the three circles.

Area subtended between the circles = Area of equilateral triangle - Area of three sectors

Side of equilateral triangle = 2r

Area of equilateral triangle = √3/4 × (2r)2 = √3r2

Area of one sector = ½ × r2 × θ

θ = 60° or π/3

Area of one sector = ½ × r2 × π/3

Area of three sectors = πr2/2

Area subtended between the circles = √3r2 - πr2/2

r = 3.5 = 7/2

Required area = 49/8 (2√3 - π)

The correct option is C.