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, given that the length of the chord is equal to the radius of the circle.

### Step-by-Step Solution:

1. **Draw the Circle**: Start by drawing a circle with center O. Label the radius as r.

2. **Draw the Chord**: Draw a chord AB such that the length of chord AB is equal to the radius r.

3. **Identify the Triangle**: Connect the endpoints of the chord (A and B) to the center O of the circle. This forms triangle OAB.

4. **Recognize the Triangle Type**: Since the lengths OA and OB are both equal to the radius (r), and AB is also equal to r, triangle OAB is an equilateral triangle.

5. **Calculate the Angles**: In an equilateral triangle, all angles are equal. Therefore, the angle ∠AOB is 60 degrees.

6. **Find the Angle Subtended in the Major Segment**: The angle subtended by the chord AB at point C on the major segment (the arc opposite the chord) can be found using the property that the angle subtended at the center is twice the angle subtended at any point on the circumference.

Therefore, the angle ∠ACB (the angle subtended by the chord in the major segment) is given by:
\[ \text{Angle in major segment} = 180^\circ - \frac{1}{2} \times \text{Angle at center} \]
\[ \text{Angle in major segment} = 180^\circ - \frac{1}{2} \times 60^\circ = 180^\circ - 30^\circ = 150^\circ \]

### Final Answer:
The angle which the chord subtends in the major segment of the circle is **150 degrees**.

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