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 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