Areas of Sector and Segment of a Circle

Let us study what is meant by sector of a circle. Fig 1.1

The circular region enclosed
by two radii and the corresponding arc is called a
sector of the circle and the portion (or part) of the
circular region enclosed between a chord and the
corresponding arc is called a segment of the circle.
Thus, in Fig1.1, shaded region OAPB is a sector
of the circle with centre O. ∠ AOB is called the
angle of the sector. Note that in this figure, unshaded region OAQB is also a sector of
the circle. For obvious reasons, OAPB is called the minor sector and
OAQB is called the major sector. You can also see that angle of the major sector is
360° – ∠ AOB.
Now, look at Fig1.2. in which AB is a chord
of the circle with centre O. So, shaded region APB is
a segment of the circle. You can also note that
unshaded region AQB is another segment of the circle
formed by the chord AB. For obvious reasons, APB
is called the minor segment and AQB is called the
major segment.
Now let us study the formula for area of a sector of a circle. Fig 1.2