JAMB Mathematics 2023 Paper

Concept:Use Pythagoras theorem, the tangent ratio, and the arc length formula.Explanation:In the right triangle $XOB$, the perpendicular from the centre $O$ meets the chord $AB$ at $X$.$OB = 13$ cm is the radius, and $XB = 12$ cm is half of the chord.Let $OX = h$. Using Pythagoras theorem:$13^2 = 12^2 + h^2$$169 = 144 + h^2$$h^2 = 25$, so $h = 5$ cm.Let $\theta = \angle XOB$. Then:$\tan \theta = \frac{XB}{OX} = \frac{12}{5} = 2.4$$\theta = \tan^{-1}(2.4) = 67.38^\circ$Since the perpendicular from the centre bisects the central angle:$\angle AOB = 2\theta = 134.76^\circ$Now calculate the arc length $AB$:$L = \frac{\angle AOB}{360^\circ} \times 2\pi r$$L = \frac{134.76}{360} \times 2 \times \frac{22}{7} \times 13$$L = 30.588$ cmCorrect to three significant figures:Answer:B. 30.6 cm