(i) Area of sector
(ii) Perimeter of sector
11. Minor sector : A sector of a circle is called a minor sector if the minor arc of the circle is a part of its boundary. In the above figure minor sector is OACB.
12. Major sector : A sector of a circle is called a major sector, if the major arc of the circle is a part of its boundary. In the above figure, OADB is the major sector.
13. The sum of the arcs of major and minor sectors of a circle is equal to the circumference of the circle.
14. The sum of the areas of major and minor sectors of a circle is equal to the area of the circle.
15. The area of a sector is given by where
16. Angle described by minute hand in minutes .
angle described by minute hand in one minute
Thus, the minute hand rotate through an angle of in one minute.
17. Angle described by hour hand in hours .
angle described by hour hand in 1 hour
Angle described by hour hand in one minute
Thus, hour hand rotates through in 1 minute.
18. A segment of a circle is the region bounded by an arc and a chord, including the arc and the chord.
19. Minor segment : If the boundary of a segment is a minor arc of a circle, then the corresponding segment is called a minor segment. In the figure, segment PQR (the are which is shaded) is a minor segment.
20. Major segment : A segment corresponding a major arc of a circle is known as the major segment. In the figure above segment PQSP is a major segment.
21. Area of minor segment PRQS
22. Area of major segment PSQ
– area of minor segment PRQ.