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

$$\large{ A = \frac{a\;b \;-\; r \; L \;+\; c \; \left(r \;-\; h\right) }{2 } }$$
Symbol English Metric
$$\large{ A }$$ = area $$\large{ft^2}$$ $$\large{m^2}$$
$$\large{ L }$$ = arc length $$\large{ft}$$ $$\large{m}$$
$$\large{ c }$$ = chord length $$\large{ft}$$ $$\large{m}$$
$$\large{ a, b }$$ = edge $$\large{ft}$$ $$\large{m}$$
$$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$
$$\large{ h }$$ = segment height $$\large{ft}$$ $$\large{m}$$

Arc Length of a Circle Corner formula

$$\large{ L = r \; \Delta }$$
Symbol English Metric
$$\large{ L }$$ = arc length $$\large{ft}$$ $$\large{m}$$
$$\large{ \Delta }$$ = angle  $$\large{deg}$$ $$\large{rad}$$
$$\large{ r }$$ = radius $$\large{ft}$$   $$\large{m}$$

Chord Length of a Circle Corner formula

$$\large{ c = a^2 \; b^2 }$$
Symbol English Metric
$$\large{ c }$$ = chord length $$\large{ft}$$ $$\large{m}$$
$$\large{ a, b }$$ = edge $$\large{ft}$$ $$\large{m}$$

Height of a Circle Corner formula

$$\large{ h = r \; \left( 1 - cos \; \frac{\Delta}{2} \right) }$$
Symbol English Metric
$$\large{ h }$$ = segment height $$\large{ft}$$ $$\large{m}$$
$$\large{ \Delta }$$ = segment angle $$\large{deg}$$ $$\large{rad}$$
$$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$

Perimeter of a Circle Corner formula

$$\large{ p = a + b + L }$$
Symbol English Metric
$$\large{ p }$$ = perimeter  $$\large{ft}$$ $$\large{m}$$
$$\large{ L }$$ = arc length $$\large{ft}$$ $$\large{m}$$
$$\large{ a, b }$$ = edge $$\large{ft}$$ $$\large{m}$$

Segment Angle of a Circle Corner formula

$$\large{ \Delta = arccos \; \frac{ 2\;r^2 \;-\; c^2 }{2\;r^2} }$$
Symbol English Metric
$$\large{ \Delta }$$ = segment angle $$\large{deg}$$ $$\large{rad}$$
$$\large{ c }$$ = chord length $$\large{ft}$$ $$\large{m}$$
$$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$