# 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.

## Formulas that use Area of 3 Overlapping Circles

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

### Where:

$$\large{ A }$$ = area

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius

## Formulas that use Perimeter of 3 Overlapping Circles

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

### Where:

$$\large{ P }$$ = perimeter

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius