Angle bisector exists and is unique

Dependencies: Protractor axiom.

Statement

Let $\angle AOB$ satisfy $0^\circ < \theta < 180^\circ$, where $\theta = \angle AOB$. Then inside $\angle AOB$ there exists a unique ray $OC$ emanating from $O$ such that

This ray $OC$ is called the bisector of $\angle AOB$.