NECO 2005 Mathematics · Question 21

A chord 20cm long subtends an angle of 60° at the circumference of a circle, what is the diameter of the circle the nearest cm?

Options

A.12cm
B.20cm
C.23cm
D.60cm
E.80cm

Answer: C. 23cm

Explanation written with AI and checked against the answer key

Analyze the question: A chord of length 20 cm subtends an angle of 60° at the circumference. We need the diameter of the circle. Concept: By the sine rule applied to a circle (extended law of sines), a chord of length c subtending an inscribed angle θ at the circumference satisfies: c / sin θ = 2R = diameter Solution: Diameter = 20 / sin 60° sin 60° = √3/2 ≈ 0.8660 Diameter = 20 / 0.8660 ≈ 23.09 cm To the nearest cm, the diameter is 23 cm. Check using the central angle: The angle at the centre is 2 × 60° = 120°. The triangle formed by the two radii and the chord is isosceles. Splitting it in half gives a right-angled triangle with angle 60° at the centre and opposite side 10 cm: sin 60° = 10 / R, so R = 10 / 0.8660 ≈ 11.55 cm Diameter = 2R ≈ 23.09 cm ≈ 23 cm Exam tip: Remember the formula chord = diameter × sin(angle at circumference). Whenever a chord and an angle at the circumference are given, use this directly and save time. Be careful not to confuse the angle at the circumference with the angle at the centre (which is double).

AI can make mistakes. Report anything that looks wrong.