Question

A chord of a circle of radius 4 cm is making an angle 60° at the centre, then the length of the chord is:

• A. 1 cm
• B. 2 cm
• C. 3 cm
• D. 4 cm

Hint:

Use the formula \(l = 2r \sin \left(\frac{\theta}{2}\right)\) to find the length of a chord, where \(r\) is the radius and \(\theta\) is the angle at the center.

Answer 1

The Correct Option is B

The length of the chord of a circle can be found using the formula: \[ l = 2r \sin \left(\frac{\theta}{2}\right) \] where \(r = 4 \, \text{cm}\) and \(\theta = 60^\circ\). Substituting the values: \[ l = 2 \times 4 \times \sin \left(\frac{60^\circ}{2}\right) = 8 \times \sin 30^\circ = 8 \times \frac{1}{2} = 4 \, \text{cm} \] Thus, the correct answer is option (4).