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?

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