Explanation:

- To find the radius \( r \) of a circle when a chord of length \( 7 \) cm subtends a \( 60^\circ \) angle at the center:

- Use the formula: chord length \( = 2r \sin(\theta/2) \), where \( \theta \) is in degrees.

- Here, \( 7 = 2r \sin(30^\circ) \).

- Since \( \sin(30^\circ) = \frac{1}{2} \), the equation becomes: \( 7 = 2r \times \frac{1}{2} \).

- \( 2r \times \frac{1}{2} = r \) so \( 7 = r \).

- Therefore, the radius is 7 cm.

- Option 1: \( 7\sqrt{2} \) ? Not correct; comes if angle or chord is different.

- Option 2: \( 7\sqrt{3} \) ? Not correct; possible if angle was \( 120^\circ \).

- Option 3: 7 Correct answer.

- Option 4: 14 ? Not correct; would require a sine of \( 0.5 \) for a much longer chord.