Arc
From Latin: arcus "a bow, arch,"
Try this Drag one of the orange dots that define the endpoints of the blue arc.
The arc will change accordingly.
An arc is a portion of the circumference of a circle.
In the figure above, the arc is the blue part of the circle.
Strictly speaking, an arc could be a portion of some other curved shape, such as an ellipse, but it almost always refers to a circle.
To avoid all possible mistake, it is sometimes called a circular arc.
A straight line is drawn between the end points of the arc would be a
chord of the circle.
If the arc length is exactly half the circle, this called a semicircular arc. See Semicircle definition.
Naming and identification
Arcs are named by their endpoints. The blue arc above would be called "arc AB". or "arc BA", the
order of the endpoints does not matter. As a shorthand this can be written as the letters AB with a curving line above them
Example:
which is read "arc AB".
Notice that this naming can be ambiguous. For example it may mean the
major arc AB,
where you go the long way around the bottom of the circle. Unless stated otherwise, it always means the
minor arc  the shortest of the two.
If you want to indicate the major arc, add an extra point and use three letters in the name. For example in the diagram on the right the major arc is indicated by
which is the long arc from A to B going around the bottom via K.
There are two measures of an arc
 The length of the arc
 The angle of the arc
Arc length
The length of an arc is the distance along the curved line forming the arc. It would be measured in distance units, such as meters. To indicate this measure, the arc is preceded by the lower case letter L (for 'length'). For eaxmaple
would be read as "the length of the arc AB is 6 inches". See Arc Length page for more.
Angle measure
The angle measure is the angle formed by the arc at the center of the circle. It is indicated by the
small letter M in front of the name. For example
is read as "the arc AB has a measure of 35 degrees".
See Arc Angle Measure for more.
Attributes
While you are here..
... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone.
However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site?
When we reach the goal I will remove all advertising from the site.
It only takes a minute and any amount would be greatly appreciated.
Thank you for considering it! – John Page
Become a patron of the site at patreon.com/mathopenref
Other circle topics
General
Equations of a circle
Angles in a circle
Arcs
(C) 2011 Copyright Math Open Reference. All rights reserved
