Circle Corner

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• Circle 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