Thales' Theorem/Proof 2

Theorem
Let $A$ and $B$ be two points on opposite ends of the diameter of a circle.

Let $C$ be another point on the circle such that $C \ne A, B$.

Then the lines $AC$ and $BC$ are perpendicular to each other.

Proof
From the Inscribed Angle Theorem, $\angle AOB = 2 \angle ACB$.

Then we have that $\angle AOB$ is a straight angle.

Hence the result.

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

On the other hand, some attribute this theorem to Pythagoras.