# Arcs

A
**
minor arc
**
is the shorter arc connecting two endpoints on a
circle
.

The
**
measure
**
of a minor arc is less than
$180\xb0$
, and equal to the measure of the arc's
central angle
.

A
**
major arc
**
is the longer arc connecting two endpoints on a circle.

The measure of a major arc is greater than $180\xb0$ , and equal to $360\xb0$ minus the measure of the minor arc with the same endpoints.

An arc measuring exactly
$180\xb0$
is called a
**
semicircle
**
.

In the figure, $m\stackrel{\u2322}{AB}=x\xb0$ and $m\stackrel{\u2322}{ACB}=\left(360-x\right)\xb0$ .

Note that the minor arc is named with just two endpoints, while the major arc is named with three letters, the two endpoints and a third point on the arc.

Adjacent arcs are arcs of the same circle that have exactly one point in common.

### Arc Addition Postulate

The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

In the circle, $\stackrel{\u2322}{PQ}$ and $\stackrel{\u2322}{QR}$ are adjacent arcs.

So, $m\stackrel{\u2322}{PQR}=m\stackrel{\u2322}{PQ}+m\stackrel{\u2322}{QR}$ .