Angle inscribed in a semicircle

Applying the central angle theorem to a particular case yields a classic result, often called Thales’ theorem on the circle.

Observation — Special case: the semicircle

If the arc $AB$ is a semicircle, the central angle is $\pi$, hence the inscribed angle is $\frac{\pi}{2}$: every angle inscribed in a semicircle is a right angle.

Links

Topics: Euclidean circle
Concepts: Inscribed angle · Semicircle
Skills: Synthetic geometry