CLASS-6
SEGMENT OF A CIRCLE
SEGMENT OF A CIRCLE -
A segment of a circle is the region bounded by a chord (a straight line connecting two points on the circle) and the arc intercepted by the chord. There are two main types of segments: minor segment and major segment.
A chord of a circle divides its circular region into two parts. Each part is called segment.
The part containing the minor arc is called minor segment, and the part containing the major arc is called the major segment.
- Minor Segment:- The minor segment is the region enclosed by a chord and the minor arc (the smaller portion of the circumference) intercepted by the chord.The area of the minor segment can be calculated using the formula:-
Area of Minor Segment = 1/2 r² (θ − sinθ)
where:
r is the radius of the circle.
θ is the central angle of the segment in radians.
2. Major Segment:- The major segment is the region enclosed by a chord and the major arc (the larger portion of the circumference) intercepted by the chord. The area of the major segment can be calculated using a similar formula:
Area of Major Segment = 1/2 r²(2π − θ + sinθ)
where:-
r is the radius of the circle.
θ is the central angle of the segment in radians.