The Circle

The following are short descriptions of the circle shown below.

Tangent - is a line that would pass through one point on the circle.
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.

 

The Circle

 

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
circular-sector.jpgLength 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
segment-of-a-circle.jpgArea 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:
$A = A_{sector} + A_{triangle}$

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

 

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