A chord of a circle has a length of 12 cm. The angle subtended by the chord at a point on the circumference is 30°. What is the distance from the center of the circle to the chord?

Correct option is A

Given :

Length of chord = 12 cm
Angle subtended by the chord at a point on the circumference = 30$$^\circ$$​​

Formula Used :

Angle at center = 2$$\times$$​ angle at circumference

Chord length formula
​$$\text{Chord} = 2R \sin\left(\frac{\theta}{2}\right)$$​​

Distance of chord from center
d = R $$\cos\left(\frac{\theta}{2}\right)$$​​

Solution :

Central angle subtended by the chord:

​$$\theta = 2 \times 30^\circ = 60^\circ$$​​​

Using chord length formula:
12 = 2R$$\sin 30^\circ$$​​
12 = 2R$$\times \frac{1}{2}$$​​
R = 12 cm

Distance of chord from center:
d = R cos $$30^\circ$$​​
d = 12 $$\times \frac{\sqrt{3}}{2}$$​​
d = 6$$\sqrt{3} \text{ cm}$$​​