The Circle

Tags: 
secant
tangent
chord
diameter
circle
sector of a circle
segment of a 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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