Circle is Bisected by Diameter/Proof 2

Proof

 * Diameter Bisects Circle.png

Let $AB$ be a diameter of a circle whose center is at $O$.

By definition of diameter, $AB$ passes through $O$.

Because $\overline{AOB}\cong\overline{BOA}$:
 * $\angle AOB\cong\angle BOA$

That is:
 * $\stackrel{\frown}{AB}\cong\stackrel{\frown}{BA}$

Hence, a circle is split into two equal arcs by a diameter.