3 Connecting Circles

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • circular arc triangle 23 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:

\(\large{ n }\) = arc length

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

\(\large{ r }\) = radius

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:

\(\large{ A_{area} }\) = area

\(\large{ i }\) = arc insert

\(\large{ n }\) = arc length

\(\large{ r }\) = radius

Insert of a Circle Arc Triangle formula

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

Where:

\(\large{ i }\) = arc insert

\(\large{ a }\) = arc

Perimeter of a Circle Arc Triangle formula

\(\large{ P = 3\;n  }\)

Where:

\(\large{ P }\) = perimeter

\(\large{ n }\) = arc length