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Circular Fun (Posted on 2005-07-28) Difficulty: 2 of 5
When you draw three circles of radius r such that all three are externally tangent, what is the area of the shape in the center in terms of r?

See The Solution Submitted by Justin    
Rating: 3.2857 (7 votes)

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No Subject | Comment 11 of 18 |

in that particular kind of geometry. joining the centres of each circles forms a equilateral Δ with side length 2r and angle 60 each.

  • area of the desired shape would be area of equilateral Δ -  3*area of circle of 60 degree section
  • area of equilateral Δ =√3 * r²
  • area of 360º = π*r²  it implies  area for 60º = π*r²/6
  • substituting back we get 
  • area of desired shape =(√3 - π/2) * r²

  Posted by devendra kumar on 2005-08-22 02:01:43
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