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 $O$.

$\angle AOB\cong\angle BOA$ because they are both straight angles.

Thus, the arcs are congruent by Equal Angles in Equal Circles:
 * $\stackrel{\frown}{AB}\cong\stackrel{\frown}{BA}$

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