The total plane angle subtended by a circle at its centre is

Options

A. `pi` rad
B. `2pi` rad
C. `(2pi)/3` rad
D. `pi/2` rad

Answer

To find the total plane angle subtended by a circle at its center, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Circle**:
- A circle is a two-dimensional shape where all points are equidistant from a central point called the center.

2. **Defining the Angle**:
- The angle subtended at the center of the circle is measured by the amount of rotation from one point on the circumference to another point on the circumference.

3. **Measuring the Angle**:
- We can measure angles in degrees or radians. A full rotation around a point is 360 degrees or \(2\pi\) radians.

4. **Calculating the Total Angle**:
- Since a complete revolution around the center of the circle corresponds to the entire circumference, the angle subtended by the circle at its center is \(360\) degrees.
- Converting \(360\) degrees to radians:
\[ 360 \text{ degrees} = 2\pi \text{ radians} \]

5. **Conclusion**:
- Therefore, the total plane angle subtended by a circle at its center is \(2\pi\) radians.

### Final Answer:
The total plane angle subtended by a circle at its center is \(2\pi\) radians.

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