The Circle
The following are short descriptions of the circle shown below.
Secant - is a line that would pass through two points on the circle.
Chord - is a secant that would terminate on the circle itself.
Diameter, d - is a chord that passes through the center of the circle.
Radius, r - is one-half of the diameter.
- Area of the circle
- $A = \pi \, r^2$
$A = \frac{1}{4}\pi \, d^2$
- Circumference of the circle
- $c = 2\pi \, r$
$c = \pi \, d$
- Sector of a Circle
Length of arc:
$s = \dfrac{\pi \, r \theta_{degree}}{180^\circ}$
$s = r \, \theta_{radians}$
Area of the sector:
$A = \dfrac{\pi \, r^2 \theta_{degrees}}{360^\circ}$$A = \frac{1}{2}r^2 \, \theta_{radians} $
$A = \frac{1}{2}sr$
- Segment of a Circle
Area of circular segment with s ½ c:
$A = A_{sector} - A_{triangle}$$A = \frac{1}{2}r^2 (\theta_{radian} - \sin \theta_{degrees})$
Area of circular segment with s > ½ c:
$A = A_{sector} + A_{triangle}$$A = \frac{1}{2}r^2 (\alpha_{radian} + \sin \theta_{degrees})$