AB is a diameter of the circle with centre O, CD is chord of the circle. If `/_BOC = 120^@`, then the value of `/_ADC` is

Options

A. `42^@`
B. `30^@`
C. `60^@`
D. `35^@`

Answer

To solve the problem, we will follow these steps:

1. **Understand the Circle and Angles**: We have a circle with diameter AB and center O. The chord CD is drawn such that angle BOC is given as 120 degrees. We need to find the angle ADC.

2. **Identify the Angles**: Since AB is the diameter, angle ACB (where C is on the circumference) will be a right angle (90 degrees) due to the inscribed angle theorem.

3. **Use the Relationship of Angles**: In triangle BOC, we know that the sum of angles in a triangle is 180 degrees. Therefore, we can express angle AOB as:
\[ \angle AOB = 180^\circ - \angle BOC = 180^\circ - 120^\circ = 60^\circ \]

4. **Find the Angles at the Circumference**: The angle ADC subtended by arc AC at point D on the circumference is half of angle AOB (because angles subtended at the center are twice those subtended at the circumference). Therefore:
\[ \angle ADC = \frac{1}{2} \times \angle AOB = \frac{1}{2} \times 60^\circ = 30^\circ \]

5. **Conclusion**: The value of angle ADC is 30 degrees.

### Final Answer:
\[ \angle ADC = 30^\circ \]

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