JAMB Mathematics 2022 Paper

Concept:A perpendicular from the centre of a circle to a chord bisects the chord.The radius forms the hypotenuse of a right-angled triangle with the half-chord and the perpendicular distance.Explanation:Let the distance from the centre to the chord be $3\, \text{cm}$.This perpendicular line meets the chord at its midpoint.The radius of the circle is $5\, \text{cm}$.Using Pythagoras' theorem in the right-angled triangle formed:$$\text{radius}^2 = (\text{distance from centre})^2 + (\text{half-chord})^2$$$$5^2 = 3^2 + (\text{half-chord})^2$$$$25 = 9 + (\text{half-chord})^2$$$$(\text{half-chord})^2 = 16$$$$\text{half-chord} = 4\, \text{cm}$$The full length of the chord is twice this value:$$\text{Chord length} = 2 \times 4 = 8\, \text{cm}$$Answer:A. $8\, \text{cm}$