WAEC Mathematics 2013 Paper

Concept:A line drawn from the centre of a circle perpendicular to a chord divides the chord into two equal parts.Explanation:Let the distance from the centre $O$ to the chord be $OM = 2$ cm. Let $M$ be the midpoint of the chord $PQ$, so chord length $PQ = 2 \times MQ$. Join $O$ to $Q$, the radius of the circle, so $OQ = 5$ cm. In right-angled $\triangle OMQ$, apply Pythagoras theorem: $$OQ^2 = OM^2 + MQ^2$$ $$5^2 = 2^2 + MQ^2$$ $$25 = 4 + MQ^2$$ $$MQ^2 = 21$$ $$MQ = \sqrt{21}\ \text{cm}$$ Therefore, the length of the chord is $$PQ = 2 \times MQ = 2\sqrt{21}\ \text{cm}$$Answer:The chord is $2\sqrt{21}$ cm long.Correct option: A. $2\sqrt{21}$ cm.