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JAMB Mathematics 2020 Paper

Question : 31

Total: 40

Solution:

Concept:

When a chord equals the radius, use the chord formula to find the central angle, then compute the arc length.

Explanation:

Let

\theta

be the central angle subtended by chord

ST

Given chord length

ST = r

and circle radius

r

Use the chord length formula:

r = 2r \sin\left(\frac{\theta}{2}\right)

Divide both sides by

2r

\sin\left(\frac{\theta}{2}\right) = \frac{1}{2}

So,

\frac{\theta}{2} = 30^\circ

, hence

\theta = 60^\circ = \frac{\pi}{3}

radians.

Arc length

ST = r \theta

= r \times \frac{\pi}{3}

= \frac{\pi r}{3}

Answer:

\frac{\pi r}{3}

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