Thales' Theorem/Proof 3

Proof
Let $D$ be the center of $ACB$.

We have that $AD$, $BD$ and $CD$ are radii of the same circle.

Thus by definition:
 * $AD = BD = CD$

Thus $\triangle ADC$ and $\triangle BDC$ are isosceles triangles.

From External Angle of Triangle equals Sum of other Internal Angles:
 * $\angle CDB = \angle ACD + \angle CAD$

Hence:

Similarly, from External Angle of Triangle equals Sum of other Internal Angles:
 * $\angle CDA = \angle BCD + \angle CBD$

Hence:

Therefore:

But $\angle CDB + \angle CDA$ equals two right angles.

Hence $\angle ACB$ is a right angle.

Legend has it that he sacrificed an ox in honour of the discovery.

On the other hand, some attribute this theorem to.