# 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

## Formulas that use Arc Length of a Circle Arc Triangle

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

### Where:

$$\large{ n }$$ = arc length

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

$$\large{ r }$$ = radius

## Formulas that use Area of a Circle Arc Triangle

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

### Where:

$$\large{ A_{area} }$$ = area

$$\large{ i }$$ = arc insert

$$\large{ n }$$ = arc length

$$\large{ r }$$ = radius

## Formulas that use Insert of a Circle Arc Triangle

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

### Where:

$$\large{ i }$$ = arc insert

$$\large{ a }$$ = arc

## Formulas that use Perimeter of a Circle Arc Triangle

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

### Where:

$$\large{ P }$$ = perimeter

$$\large{ n }$$ = arc length