Circle Corner

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • circle corner 1Circle corner (a two-dimensional figure) is a right triangle having acute vertices on a circle with the hypotenuse outside the circle.
  • Chord is a line segment on the interior of a circle.
  • Segment of a circle is an interior part of a circle bound by a chord and an arc.

area of a Circle Corner formula

\(\large{ A_{area} = \frac{a\;b \;-\; r \; l \;+\; s \; \left(r \;-\; h\right)  }{2 }   }\)

Where:

\(\large{ A_{area} }\) = area

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

\(\large{ s }\) = chord length

\(\large{ a, b }\) = edge

\(\large{ r }\) = radius

\(\large{ h }\) = segment heigh

Arc Length of a Circle Corner formula

\(\large{ l =  r \; \theta  }\)

Where:

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

\(\large{ \theta }\) = angle

\(\large{ r }\) = radius

Chord Length of a Circle Corner formula

\(\large{ s = a^2 \; b^2   }\)

Where:

\(\large{ s }\) = chord length

\(\large{ a, b }\) = edge

Height of a Circle Corner formula

\(\large{ h = r \; \left( 1 - cos \; \frac{\theta}{2} \right)    }\)

Where:

\(\large{ h }\) = segment height

\(\large{ \theta }\) = segment angle

\(\large{ r }\) = radius

Perimeter of a Circle Corner formula

\(\large{ p = a + b + l   }\)

Where:

\(\large{ p }\) = perimeter

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

\(\large{ a, b }\) = edge

Segment Angle of a Circle Corner formula

\(\large{ \theta =   arccos \;  \frac{ 2\;r^2 \;-\; s^2 }{2\;r^2}  }\)

Where:

\(\large{ \theta }\) = segment angle

\(\large{ s }\) = chord length

\(\large{ r }\) = radius