The diameter of a circle is $AB$. Point $C$ is on the circumference. What is the measure of $\angle ACB$?
Explain your reasoning.

$\angle ACB = 90^\circ$

Reason: Since the angle subtended by a diameter at any point on the circle is $90^{\circ}$.
The diameter $AB$ subtends a straight angle ($180^{\circ}$) at the centre, so the angle it subtends at any point $C$ on the circle is $\frac{180^{\circ}}{2} = 90^{\circ}$.

Caution
Students should remember that the angle in a semicircle is $90^{\circ}$ only when the chord is a diameter; they must first check that the chord passes through the centre.