A circular arc, usually called simply an arc in plane geometry, is either of the two connected portions of the circumference of a circle
determined by two distinct points on it. The circular arc
corresponding to the central angle 
is denoted 
. Similarly, the size of the central
angle subtended by this arc, i.e., the measure of the arc, is sometimes (e.g.,
Rhoad et al. 1984, p. 421) but not always (e.g., Jurgensen 1963) denoted
.
The center of a circular arc is the center of the circle of which it is a part. A circular arc subtending
a central angle of 
is a quarter circle.
A circular arc whose endpoints lie on a diameter of
a circle is a semicircle.
Together with its diameter, a semicircle
bounds a half-disk; together with two perpendicular
radii, a quarter circle
bounds a quarter-disk.
For a circle of radius 
, the arc length 
subtended by a central
angle 
is proportional to 
.
If 
is measured in radians,
then the constant of proportionality is 1, so
 |
(1)
|
The length of the chord connecting the arc's endpoints is
 |
(2)
|
As Archimedes proved, for chords 
and 
which are perpendicular
to each other,
 |
(3)
|
(Wells 1991).
