An arc is a part of the circle. The intercepted arc of an angle is determined by the two points of intersection of the angle with the circle.

Measurement by central angle, The arc AB is intercepted by the central angle

$\angle$AOB. The smaller arc is called as minor arc (red arc) and the larger arc is called as major arc (blue arc)

Arcs are measured in two ways

1)

As the measure of the central angle Here, the minor arc measures 120º

The major arc measures 240º

2)

The length of the arcMeasurement by arc length (radians). If r is the radius of the circle and θ is the central angle in radians, then the length of the arc can be obtained using the formula:

S = r$\theta$ Minor arc: $\theta$ =

$\frac{2 \pi}{3}$, r = 2

Length of the red arc: S =

$\frac{2 \pi}{3}$ $\times$ 2 =

$\frac{4 \pi}{3}$ Major arc: $\theta$ =

$\frac{4 \pi}{3}$, r = 2

Length of blue arc: s = 2 $\times$ 4

$\frac{pi}{3}$ = 8

$\frac{pi}{3}$
→ Read More