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The angle subtended at the centre by a chord of a circle radius 6cm is...

Mathematics
WAEC 1994

The angle subtended at the centre by a chord of a circle radius 6cm is 120°. Find the length of the chord.

  • A. 3cm
  • B. 6cm
  • C. \(4\sqrt{2}\) cm
  • D. \(3\sqrt{3}\) cm
  • E. \(6\sqrt{3}\) cm
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Correct Answer: Option E
Explanation

\(\frac{r}{6} = \sin 60 \)

\(r = 6 \sin 60\)

= \(6 \times \frac{\sqrt{3}}{2}\)

= \(3\sqrt{3}\)

Chord = 2r = \( 2 \times 3\sqrt{3}\)

= \(6\sqrt{3}\)


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