1. Have a look here: Inscribed angle - Wikipedia, the free encyclopedia
2. As far as I understand your question you have to evaluate the length of the radius first. Use the indicated right triangle. Keep in mind that $\displaystyle \sin(60^\circ) = \frac12 \sqrt{3}$
3. To determine the length of C use proportions:
$\displaystyle \frac C{2 \pi r} = \frac{120^\circ}{360^\circ} = \frac13$
Divide triangle into two right angled triangles
Let r=radius. So sin60=3/r root3/2=3/r r=6/root3=6root3/3=2root3
area sector 1/3pir^2 =1/3pi.12=4p
Let height of triangle =h Then tan60=3/h h=3/tan60=root3
Area of triangle=1/2.6.root3=3root3
Segment=sector-triangl
That's not what's asked for, Biff.
The problem, PROPERLY worded:
chord AB = 6 cm
angle AOB = 120 degrees
calculate length of arc ACB
...to which Earboth shows the steps to solution.
An arc SUPPORTS a central angle; is NOT equal to a number of degrees:
it has its own length, which is part of the circle's circumference.