A chord of a circle subtends an angle of 60o at the length of a circle of radius 14 cm. Find the length of the chord

  • A 7 cm
  • B 14 cm
  • C 21 cm
  • D 28 cm

The correct answer is B. 14 cm

When a chord of a circle subtends an angle at the center of the circle, the length of the chord can be found using the formula:

\( \text{Length of chord} = 2 \times \text{radius} \times \sin\left(\frac{\text{angle}}{2}\right) \)

Given that the radius of the circle is 14 cm and the angle subtended at the center is 60°, we can substitute these values into the formula:

\( \text{Length of chord} = 2 \times 14 \times \sin\left(\frac{60}{2}\right) \)

\( \text{Length of chord} = 28 \times \sin(30) \)

Now, we know that \(\sin(30°) = \frac{1}{2}\), so:

\( \text{Length of chord} = 28 \times \frac{1}{2} = 14 \text{ cm} \)

Therefore, the length of the chord is 14 cm.

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