JAMB Mathematics 2013 Paper

Concept:The length of a chord which subtends an angle $\theta$ at the centre of a circle is given by the formula$$L = 2r\sin\left(\frac{\theta}{2}\right)$$Explanation:From the question, the radius is $r = 8$ cm.The angle subtended at the centre is $\theta = 90^\circ$.Substitute these values into the chord formula:$$L = 2 \times 8 \times \sin\left(\frac{90^\circ}{2}\right)$$This gives$$L = 16 \times \sin(45^\circ)$$We know that $\sin(45^\circ) = \frac{\sqrt{2}}{2}$.Therefore,$$L = 16 \times \frac{\sqrt{2}}{2}$$Simplifying,$$L = 8\sqrt{2} \text{ cm}$$This corresponds to option D.Answer:The length of the chord is $8\sqrt{2}$ cm.Correct option: D.