JAMB Mathematics 2023 Paper

Concept:The perpendicular from the centre of a circle to a chord bisects the chord.So the distance $12$ cm is the perpendicular distance from the centre to the midpoint of the chord.Explanation:Let the chord be $AB$ and let $M$ be its midpoint.Then $OM = 12\text{ cm}$ and $OA = 13\text{ cm}$.In right-angled triangle $OMA$, apply Pythagoras theorem:$$OA^2 = OM^2 + AM^2$$$$13^2 = 12^2 + AM^2$$$$169 = 144 + AM^2$$$$AM^2 = 25$$$$AM = 5\text{ cm}$$Since $OM$ bisects chord $AB$, we have:$$AB = AM + MB = 5 + 5 = 10\text{ cm}$$Answer:The length of the chord is $10\text{ cm}$.