If the length of a chord of a circle is equal to its radius, then find the angle subtended by it at the minor arc of the circle.

Answer

To solve the problem, we need to find the angle subtended by a chord at the minor arc of the circle when the length of the chord is equal to the radius of the circle.

### Step-by-Step Solution:

1. **Draw the Circle and Label the Points:**
- Draw a circle and label the center as \( O \).
- Let the chord be \( AB \) such that the length of chord \( AB \) is equal to the radius \( OA \) (or \( OB \)) of the circle.

2. **Identify the Triangle:**
- Since \( OA = OB = AB \), triangle \( OAB \) is formed.
- Here, \( OA \) and \( OB \) are the radii of the circle, and \( AB \) is the chord.

3. **Determine the Type of Triangle:**
- Since all three sides of triangle \( OAB \) are equal, triangle \( OAB \) is an equilateral triangle.

4. **Calculate the Angles of the Triangle:**
- In an equilateral triangle, each angle measures \( 60^\circ \).
- Therefore, \( \angle AOB = 60^\circ \).

5. **Find the Reflex Angle:**
- The reflex angle \( AOB \) (the angle around the center not included in triangle \( OAB \)) can be calculated as:
\[ \text{Reflex } AOB = 360^\circ - 60^\circ = 300^\circ \]

6. **Calculate the Angle at the Minor Arc:**
- The angle subtended at any point on the circumference (like point \( C \) on the minor arc) is half of the angle at the center.
- Therefore, the angle \( ACB \) (the angle subtended by chord \( AB \) at point \( C \)) is:
\[ ACB = \frac{1}{2} \times \text{Reflex } AOB = \frac{1}{2} \times 300^\circ = 150^\circ \]

### Final Answer:
The angle subtended by the chord \( AB \) at the minor arc \( ACB \) is \( 150^\circ \).

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