- Area of the Sector and Circular Segment
- Length of an Arc
1) Sector- The portion (or part) of the circular region enclosed by two radii and the corresponding arc is called a sector of the circle.
Here, OAPB is the minor sector and OAQB is the major sector.
Let OAPB be a sector of a circle with centre O and radius r. Let the degree measure of ∠AOB be θ.
Now, area of a circle= `πr^2`
We can consider this circular region to be a sector forming an angle of 360° at the centre O.
When angle at the centre is 360, area of the sector= `πr^2`
when angle at the centre is 1, area of the sector= `(πr^2)/360`
So, when angle at the centre is θ.
area of the sector= `(πr^2)/360 xx θ`
area of the sector= `θ/360 xx πr^2`
2) Segment- The potion (or part) of the circular region enclosed between a chord and the corresponding arc is called a segment of the circle.
arc APB is the minor segment and arc AQB is the major segment.
Here, in a circle with centre O and radius r, You can see that:
Area of the segment APB = Area of the sector OAPB- Area of ΔOAB
`"Area" "of" "the" "segment" "APB" =θ/360 xx πr^2- "Area" "of" "ΔOAB"`