Length of Chord in a Circle

In a circle with center O, a radius of length 10 units, and two points A and B on its circumference, the angle AOB measures 120 degrees. A line segment AB is drawn across the circle.

Using the Law of Cosines, find the length of the chord AB. Recall that the Law of Cosines states:

$$c^2 = a^2 + b^2 - 2ab \cos(C)$$

where $C$ is the included angle between sides $a$ and $b$. Here, both $a$ and $b$ are equal to the radius of the circle.