The chord of a circle is equal to its radius, find the angle subtended by this chord at the centre.

Explanation

To solve the problem where the chord of a circle is equal to its radius and we need to find the angle subtended by this chord at the center, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
We have a circle with center O. The chord AB is given to be equal to the radius OA (or OB). Let's denote the radius as R.

2. **Identify the Triangle Formed**:
The points A and B along with the center O form triangle AOB.

3. **Set Up the Sides of the Triangle**:
Since AB (the chord) is equal to the radius OA and OB, we can write:
- AB = OA = OB = R

4. **Classify the Triangle**:
Since all three sides of triangle AOB are equal (AB = OA = OB), triangle AOB is an equilateral triangle.

5. **Determine the Angles of the Triangle**:
In an equilateral triangle, all angles are equal. The sum of angles in any triangle is 180 degrees. Therefore, each angle in triangle AOB is:
\[ \text{Angle AOB} = \text{Angle A} = \text{Angle B} = \frac{180^\circ}{3} = 60^\circ \]

6. **Conclusion**:
The angle subtended by the chord AB at the center O (which is angle AOB) is 60 degrees.

### Final Answer:
The angle subtended by the chord at the center is **60 degrees**.

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