Length of Segment OP in Circle Geometry

Consider a circle with center O and a radius of 10 units. Points A and B lie on the circumference such that the line segment AB subtends an angle of 120 degrees at the center O. A point P is the midpoint of the arc AB that does not contain point O. Determine the length of segment OP.

To solve this problem, you can use the Law of Cosines in triangle OAB. The formula states:

$$c^2 = a^2 + b^2 - 2ab imes ext{cos}( heta)$$

where $c$ is the side opposite angle $θ$, and $a$ and $b$ are the other two sides.