Question

A chord of a circle of radius 6 cm is making an angle 60º at the centre. Then the length of the chord is

• A. 3 cm
• B. 6 cm
• C. 12 cm
• D. \(3\sqrt{3}\) cm

Answer 1

The Correct Option is B

Given: A chord of a circle with radius \( r = 6 \) cm subtends an angle \( 60^\circ \) at the center.

Step 1: Use chord length formula 

\[ \text{Chord Length} = 2r \sin \frac{\theta}{2} \] where \( r = 6 \) cm and \( \theta = 60^\circ \).

Step 2: Substitute values

\[ \text{Chord Length} = 2(6) \sin \frac{60^\circ}{2} \] \[ = 12 \sin 30^\circ \] \[ = 12 \times \frac{1}{2} = 6 \text{ cm} \]

Final Answer: 6 cm

Answer 2

To find the length of the chord in a circle with radius \( r = 6 \, \text{cm} \) and central angle \( \theta = 60^\circ \), we can use the chord length formula:

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

Substituting the given values:

\[ L = 2 \times 6 \times \sin\left(\frac{60^\circ}{2}\right) \]

\[ L = 12 \times \sin(30^\circ) \]

We know \(\sin(30^\circ) = \frac{1}{2}\). Thus:

\[ L = 12 \times \frac{1}{2} = 6 \, \text{cm} \]

The length of the chord is 6 cm.