Sector

                  Minor arc                                                          Major arc

What is sector?

A sector is the part of a circle enclosed by any two radii of the circle and
their intercepted arc.

Angle of sector (Central angle of sector)

Central Angle is the angle subtended by the arc of the sector at the centre
of the circle in which the sector forms a part.

A semi- circle is a sector whose central angle is 180 degree.
A quadrant of a circle is a sector whose central angle is
90 degree .

Image result for semicircle and quarter circle

  Quadrant  (90 degree)                                semicircle (180 degree)

Length of the arc (l)

Arc length of a sector POQ is the length of the portion on the circumference of the circle intercepted between the bounding radii (OP and OQ) and is denoted by l.

Area of the sector

Relationship between area of the sector and its length of arc

Perimeter of a sector

NOTE:

 

Example problems

Question 1

Question 2