# 3 Overlapping Circles

Written by Jerry Ratzlaff on . Posted in Plane Geometry

•  3 overlapping circles (a two-dimensional figure) with equal length arcs connecting at the vertices.  ## Area of 3 Overlapping Circles formulas

 $$\large{ A_1 = \left(3 \; \pi \; r^2\right) - \left(3 \; A_3\right) + A_4 }$$ $$\large{ A_2 = \left(3 \; A_3\right) - \left(2 \; A_4\right) }$$ $$\large{ A_3 = \left[ \left(2 \; \frac{\pi}{3} \right) - \sqrt{ \frac{3}{4} }\;\; \right] \; r^2 }$$ $$\large{ A_4 = \left( \pi - \sqrt{3}\; \right) \; \frac{r^2}{2} }$$

### Where:

 Units English SI $$\large{ A }$$ = area $$\large{ft^2}$$ $$\large{m^2}$$ $$\large{ \pi }$$ = Pi $$\large{dimensionless}$$ $$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$

## Perimeter of 3 Overlapping Circles formulas

 $$\large{ P_1 = 3 \; \pi \; r }$$ $$\large{ P_2 = 2 \; \pi \; r }$$ $$\large{ P_3 = \frac{4}{3} \; \pi \; r }$$ $$\large{ P_4 = \pi \; r }$$

### Where:

 Units English SI $$\large{ P }$$ = perimeter $$\large{ft}$$ $$\large{m}$$ $$\large{ \pi }$$ = Pi $$\large{dimensionless}$$ $$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$