To identify the correct description of a segment of a circle, let's understand some key terms and concepts related to a circle and its parts:
1. Radius: A line segment from the center of the circle to any point on the circle.
2. Chord: A line segment with both endpoints on the circle.
3. Arc: A part of the circumference of the circle. There are two types of arcs:
- Minor Arc: The smaller arc between two points on the circle.
- Major Arc: The larger arc between two points on the circle.
4. Sector: A region enclosed by two radii and an arc of the circle.
5. Segment: A region enclosed by a chord and the arc that lies between the endpoints of the chord.
Let's analyze each statement provided:
1. First Statement: “A segment is a portion of a sector that is bound by a radius and the minor arc formed by that radius.”
- This describes a sector, not a segment. A sector is indeed bound by radii and arcs, but a segment involves a chord, not a radius.
2. Second Statement: “A segment is a portion of a sector that is bound by a radius and the major arc formed by that radius.”
- Like the first statement, this also describes a sector. A segment specifically involves a chord, not radii.
3. Third Statement: “A segment is a portion of a sector that is bound by a chord and the minor arc formed by that chord.”
- This correctly describes a segment. A segment is the area inside the circle that is enclosed by a chord and the minor arc that the chord subtends.
4. Fourth Statement: “A segment is a portion of a sector that is bound by a chord and the major arc formed by that chord.”
- This states that a segment is bound by a chord and a major arc, which is not the standard definition of a segment as it focuses on the minor arc.
Given these analyses, the third statement is the best description of a segment of a circle:
A segment is a portion of a sector that is bound by a chord and the minor arc formed by that chord.
Thus, the correct answer is:
3
