Chapter 11 · Question 1

Define the terms (i) sector of a circle, (ii) segment of a circle. Distinguish between minor and major sectors and segments.

Answer Revealed

Direct Answer:

(i) Sector: The region of a circle enclosed by two radii and the corresponding arc is called a sector. (ii) Segment: The region of a circle enclosed between a chord and the corresponding arc is called a segment. The minor sector is the smaller region bounded by the two radii and the minor arc. The major sector is the larger region bounded by the two radii and the major arc. Similarly, the minor segment is the smaller region between a chord and the minor arc, and the major segment is the larger region between a chord and the major arc. Unless stated otherwise, 'sector' and 'segment' refer to the minor sector and minor segment.

Simple Explanation

A sector is like a pizza slice — the area between two radii. A segment is the area between a chord (a line cutting across) and the curved arc. The smaller version of each is called 'minor' and the larger is called 'major'.

Exam-Ready Structure

(i) Sector of a Circle: The portion (or part) of the circular region enclosed by two radii and the corresponding arc is called a sector. If the arc is the minor arc, the region is the minor sector. If the arc is the major arc, the region is the major sector. The angle formed by the two radii is called the angle of the sector. (ii) Segment of a Circle: The portion (or part) of the circular region enclosed between a chord and the corresponding arc is called a segment. When the region is bounded by a chord and the minor arc, it is the minor segment. When bounded by the chord and the major arc, it is the major segment. Convention: When we say 'sector' or 'segment', we mean the minor sector and the minor segment, respectively, unless stated otherwise. Key distinction: A sector involves an angle at the centre; a segment involves a chord.

Key Points

Sector: region bounded by two radii and an arc (like a pizza slice)
Segment: region bounded by a chord and an arc
Minor = smaller region, Major = larger region
By convention, 'sector' and 'segment' mean the minor ones

Define the terms (i) sector of a circle, (ii) segment of a circle. Distinguish between minor and major sectors and segments.