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?
(In reply to solution..... :)
When 3 circles of equal radius are externally tangent to one another, an equallateral triangle with sides of 2R is formed by drawing lines through their center points. Thus: area of the triangle = (2R)(2R cosR)(1/2).
Each corner of the triangle is digging into 1/6 of each circle. Thus: the area of each slice of pie = ð R² /6.
Sence there are 3 "slices of pie" inside the traingle, then the remainder or, the shape in the center, would be:
(2R)(2R cosR)(1/2) - (ð R² /6)(3)