Question

The angle in the minor segment is

• A. obtuse
• B. acute
• C. 90°
• D. None of these

Answer 1

The Correct Option is A

To solve the problem, we need to determine the nature of the angle in the major segment of a circle. Let us analyze this step by step.

1. Understanding the Major Segment:
A major segment is the larger region of a circle that is bounded by a chord and the arc subtended by that chord. The key property here is the relationship between the angle subtended by the chord at the center of the circle and the angle subtended by the same chord at any point on the circumference of the circle.

2. Key Property of Angles in a Circle:
The angle subtended by a chord at the center of the circle is twice the angle subtended by the same chord at any point on the circumference. Mathematically, if \( \theta \) is the angle subtended at the center and \( \alpha \) is the angle subtended at the circumference, then:

$$ \theta = 2\alpha $$

In the context of the major segment, the angle subtended at the center (\( \theta \)) is greater than \( 180^\circ \) because the major segment is defined as the larger part of the circle. Therefore, the angle subtended at the circumference (\( \alpha \)) must be greater than \( 90^\circ \).

3. Nature of the Angle in the Major Segment:
An angle greater than \( 90^\circ \) but less than \( 180^\circ \) is classified as an obtuse angle. Hence, the angle in the major segment is always obtuse.

Final Answer:
The correct option is \( {\text{obtuse}} \).