WAEC 2024 · Paper 1 · Q23

In the diagram, $O$ is the centre of the circle. If $|\overline{OA}| = 25\text{ cm}$ and $|\overline{AB}| = 40\text{ cm}$ , find $|\overline{OH}|$ .

The paper marks this diagram “not drawn to scale”; the redraw uses the true measurements.

Worked solution (try it first)

The perpendicular from the centre to a chord bisects it, so $|AH| = 40 \div 2 = 20$ cm.
Triangle $OHA$ has a right angle at $H$ and hypotenuse $OA = 25$ .
Pythagoras: $|OH|^2 = 25^2 - 20^2 = 225$ .
So $|OH| = 15$ cm, option A.