Thales' theorem — the inscribed angle on a diameter is 90°

Depends on: inscribed angle = central angle / 2 (Central angle is twice the inscribed angle on the same arc).

Statement

Let $\odot O$ be any circle, $AB$ one of its diameters, and $C$ any point on the circle other than $A$ and $B$. Then the inscribed angle

In other words, as $C$ slides along the circle (without coinciding with the endpoints), $\angle ACB$ is always a right angle — this is the famous Thales circle.