The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends in the major segment of the circle is equal to :

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

To solve the problem, we need to find the angle that the chord subtends in the major segment of the circle when the length of the chord is equal to the radius of the circle.

### Step-by-step Solution:

1. **Identify the Given Information:**
- Let the radius of the circle be \( r \).
- The length of the chord \( AB \) is also equal to \( r \).

2. **Form a Triangle:**
- Consider the center of the circle as point \( O \).
- The points \( A \) and \( B \) are the endpoints of the chord.
- Since \( OA = OB = AB = r \), triangle \( OAB \) is formed.

3. **Determine the Type of Triangle:**
- Since all three sides of triangle \( OAB \) are equal, triangle \( OAB \) is an equilateral triangle.
- Therefore, each angle in triangle \( OAB \) is \( 60^\circ \).

4. **Identify the Angles:**
- Let \( \angle AOB = 60^\circ \).
- We need to find the angle \( ACB \) that the chord \( AB \) subtends in the major segment of the circle.

5. **Use the Circle Theorem:**
- According to the theorem, the angle subtended at the center of the circle (which is \( \angle AOB \)) is twice the angle subtended at any point on the circumference (which is \( \angle ACB \)).
- Therefore, we have the relationship:
\[ \angle AOB = 2 \times \angle ACB \]

6. **Substitute the Known Values:**
- Substitute \( \angle AOB = 60^\circ \) into the equation:
\[ 60^\circ = 2 \times \angle ACB \]

7. **Solve for \( \angle ACB \):**
- Divide both sides by 2:
\[ \angle ACB = \frac{60^\circ}{2} = 30^\circ \]

8. **Conclusion:**
- The angle which the chord \( AB \) subtends in the major segment of the circle is \( 30^\circ \).

### Final Answer:
The angle which the chord subtends in the major segment of the circle is \( 30^\circ \).

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