# 3 Connecting Circles

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• 3 connecting circles (a two-dimensional figure) has three equal length arcs connecting at the vertices bound by circles.
• a = b = c
• 3 arcs
• 3 vertexs

## Arc Length of a Circle Arc Triangle formula

 $$\large{ n = \frac{\pi}{3} \;r }$$

### Where:

 Units English SI $$\large{ n }$$ = arc length $$\large{ft}$$ $$\large{m}$$ $$\large{ \pi }$$ = Pi $$\large{dimensionless}$$ $$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$

## Area of a Circle Arc Triangle formula

 $$\large{ A_{area} = \frac{ \left( \sqrt{ \frac{3}{2} } \;+\; 3 \right) \; r^2 \;-\; 3\;r\;n \;-\; 3\;r\;i }{2} }$$

### Where:

 Units English SI $$\large{ A_{area} }$$ = area $$\large{ft^2}$$ $$\large{m^2}$$ $$\large{ i }$$ = arc insert $$\large{ft}$$ $$\large{m}$$ $$\large{ n }$$ = arc length $$\large{ft}$$ $$\large{m}$$ $$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$

## Insert of a Circle Arc Triangle formula

 $$\large{ i = 1 - \sqrt{ \frac{3}{2} } \; r }$$

### Where:

 Units English SI $$\large{ i }$$ = arc insert $$\large{ft}$$ $$\large{m}$$ $$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$

## Perimeter of a Circle Arc Triangle formula

 $$\large{ P = 3\;n }$$

### Where:

 Units English SI $$\large{ P }$$ = perimeter $$\large{ft}$$ $$\large{m}$$ $$\large{ n }$$ = arc length $$\large{ft}$$ $$\large{m}$$