3 Overlapping Circles

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • 3 overlapping circles 23 overlapping circles 1A3 overlapping circles (a two-dimensional figure) with equal length arcs connecting at the vertices.

Area of 3 Overlapping Circles formula

\(\large{ A_1 = \left(3 \; \pi \; r^2\right) - \left(3 \; A_2\right) + A_1  }\)

\(\large{ A_2 = \left(3 \; A_2\right) - \left(2 \; A_1\right)  }\)

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

\(\large{ A_4 = \left( \pi - \sqrt{3}\; \right) \; \frac{r^2}{2}  }\)

Where:

\(\large{ A }\) = area

3 overlapping circles 43 overlapping circles 3\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius

Perimeter of 3 Overlapping Circles formula

\(\large{ P_1 = 3 \; \pi \; r  }\)

\(\large{ P_2 = 2 \; \pi \; r  }\)

\(\large{ P_3 = \frac{4}{3} \; \pi \; r  }\)

\(\large{ P_4 = \pi \; r  }\)

Where:

\(\large{ P }\) = perimeter

\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius