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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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Solution A triangle | Comment 1 of 18
The three centres are 2R apart and form an equilateral triangle of area √3*R^2

The three sectors whose centres are at the vertices of this triangle form the area of half a circle of radius R ( area is π*Rē/2   --- The 'n' looking shape is Pi)

The area of the internal "triangle" is therefore:
√3*R^2 - π*Rē/2 
= Rē(2√3 - π)/2
  Posted by brianjn on 2005-07-28 06:15:37
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