# 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
$A = A_{sector} - A_{triangle}$
$A = \frac{1}{2}r^2 (\theta_{radian} - \sin \theta_{degrees})$

Area of circular segment with s > ½ c:

$A = A_{sector} + A_{triangle}$$A = \frac{1}{2}r^2 (\alpha_{radian} + \sin \theta_{degrees})$