A chord of a circle of radius 12 cm subtends an angle of 60° at the centre. Find the area of the corresponding segment of the circle.
( Use `pi = 3.14, sqrt(3) = 1.73` )

Answer

To find the area of the segment of a circle defined by a chord that subtends an angle of 60° at the center of a circle with a radius of 12 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Radius of the circle (r) = 12 cm
- Central angle (θ) = 60°

2. **Calculate the Area of the Sector:**
The formula for the area of a sector is given by:
\[ \text{Area of Sector} = \frac{\pi r^2 \theta}{360} \]
Substituting the values:
\[ \text{Area of Sector} = \frac{3.14 \times (12)^2 \times 60}{360} \]
\[ = \frac{3.14 \times 144 \times 60}{360} \]
\[ = \frac{3.14 \times 8640}{360} \]
\[ = \frac{27178.4}{360} = 75.49 \text{ cm}^2 \]

3. **Calculate the Area of Triangle OAC:**
Since triangle OAC is an isosceles triangle with two sides equal to the radius (12 cm) and the angle at the center being 60°, it is also an equilateral triangle.
The area of an equilateral triangle can be calculated using the formula:
\[ \text{Area} = \frac{\sqrt{3}}{4} a^2 \]
where \( a \) is the length of a side. Here, \( a = 12 \) cm.
\[ \text{Area of Triangle OAC} = \frac{\sqrt{3}}{4} \times (12)^2 \]
\[ = \frac{\sqrt{3}}{4} \times 144 = 36\sqrt{3} \]
Using \( \sqrt{3} = 1.73 \):
\[ = 36 \times 1.73 = 62.28 \text{ cm}^2 \]

4. **Calculate the Area of the Segment:**
The area of the segment is given by:
\[ \text{Area of Segment} = \text{Area of Sector} - \text{Area of Triangle OAC} \]
Substituting the values calculated:
\[ \text{Area of Segment} = 75.49 - 62.28 = 13.21 \text{ cm}^2 \]

### Final Answer:
The area of the corresponding segment of the circle is approximately **13.21 cm²**.