Circle is Bisected by Diameter
By definition of diameter, $AB$ passes through $C$.
Thus it will be possible to find a diameter $DE$ passing through $C$ such that $DC \ne CE$.
Both $DC$ and $CE$ are radii of $ADBE$.
- A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another;
- And the point is called the center of the circle.
That is, all radii of $ADBE$ are equal.
But $DC \ne CE$.
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:
- A diameter of the circle is any straight line drawn through the center and terminated in both directions by the circumference of the circle, and such a straight line also bisects the center.