3 Overlapping Circles

• 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	\(\large{ft}\)	\(\large{m}\)