| | | d = 2r
C = 2 Pi r = Pi d
K = Pi r2 = Pi d2/4
C = 2 sqrt(Pi K)
K = C2/4 Pi =
| 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 semi-circle.)
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(r2-d2) = 2r sin(theta/2) = 2d tan(theta/2) = 2 sqrt[h(2r-h)]
d = sqrt(4r2-c2)/2 = r cos(theta/2) = c cot(theta/2)/2
K = r2[theta-sin(theta)]/2 = r2arccos([r-h]/r) - (r-h)sqrt(2rh-h2)
= r2arccos(d/r) - d sqrt(r2-d2)
theta = s/r
K = r2[s/r - sin(s/r)]/2
Sector of a Circle
|
| | | The pie-shaped piece of a circle 'cut out' by two radii.
Central angle:
theta (in radians),
alpha (in degrees)
Area: K
Arc length: s
K = r2theta/2 = r2alpha Pi/360
theta = s/r
K = rs/2 |
|
|
