The angle subtended by a minor arc in its alternate segment is…………….

Options

A. acute
B. obtuse
C. `90^(@)`
D. reflex angle.

Explanation

To solve the question, "The angle subtended by a minor arc in its alternate segment is...", we need to understand the properties of circles and angles related to arcs.

### Step-by-Step Solution:

1. **Understanding the Circle and Arcs**:
- Consider a circle with center O. Let A and B be two points on the circumference of the circle, forming a minor arc AB.
- The minor arc AB is the smaller arc connecting points A and B.

2. **Identifying the Segments**:
- The circle is divided into two segments by the chord AB. The segment that contains the arc AB is called the minor segment, and the other segment is called the major segment.

3. **Angle Subtended by the Arc**:
- The angle subtended by the minor arc AB at any point on the circumference of the circle in the major segment is what we are interested in. Let’s denote this angle as ∠ACB, where C is any point on the circumference of the major segment.

4. **Using the Alternate Segment Theorem**:
- According to the Alternate Segment Theorem, the angle subtended by a minor arc at any point in the alternate segment (the major segment in this case) is equal to the angle subtended by the chord at the center of the circle.
- This angle is always an acute angle (less than 90 degrees).

5. **Conclusion**:
- Therefore, the angle subtended by a minor arc in its alternate segment is an acute angle.

### Final Answer:
The angle subtended by a minor arc in its alternate segment is an acute angle.

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