Perpendicular Bisectors

Draw another radius connecting $O$ and a random point between $A, B$.

Find the midpoint of $\overline{AB}$, and then connect that point with $O$.

The angle bisector of $\angle AOB$ is also the perpendicular bisector of $\overline{AB}$.

Draw a random line that is perpendicular to $\overline{AB}$.

Find a line that is perpendicular to $\overline{AB}$ and has $O$ on it.