also see Defining Geometric Figures
Circle 


All points on the circumference of a circle
are equidistant from its center.
Radius: r
Diameter: d
Circumference: C
Area: K



d = 2r
C = 2 Pi r = Pi d
K = Pi r^{2} = Pi d^{2}/4
C = 2 sqrt(Pi K)
K = C^{2}/4 Pi = Cr/2 


To read about circles, visit The
Geometry Center.

Arc of a Circle 


A curved portion of a circle.
Length: s
Central angle:
theta (in radians),
alpha (in degrees)
s = r theta = r alpha Pi/180 
Segment of a Circle



Either of the two regions
into which a secant or a chord cuts a
circle. (However, the formulas below assume that
the segment is no larger than a semicircle.)
Chord length: c
Height: h
Distance from center of circle to chord's midpoint: d
Central angle: theta (in radians), alpha (in degrees)
Area: K
Arc length: s 

theta = 2 arccos(d/r) = 2 arctan(c/(2d)) = 2 arcsin(c/(2r))
h = r  d
c = 2 sqrt(r^{2}d^{2}) = 2r sin(theta/2)
= 2d tan(theta/2) = 2 sqrt[h(2rh)]
d = sqrt(4r^{2}c^{2})/2 = r cos(theta/2) =
c cot(theta/2)/2
K = r^{2}[thetasin(theta)]/2 = r^{2}arccos([rh]/r)
 (rh)sqrt(2rhh^{2})
= r^{2}arccos(d/r)
 d sqrt(r^{2}d^{2})
theta = s/r
K = r^{2}[s/r  sin(s/r)]/2
For much more about segments of circles, see
The Arc, Chord, Radius, Height, Angle, Apothem, and Area.

Sector of a Circle



The pieshaped piece of a circle 'cut out' by two radii.
Central angle:
theta (in radians),
alpha (in degrees)
Area: K
Arc length: s
K = r^{2}theta/2 = r^{2}alpha
Pi/360
theta = s/r
K = rs/2 
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