- Perimeter (circumference) of a circle with diameter d (d = 2r, where r is the radius) is given by C = d = 2r
- Perimeter of semicircle with radius
- Area of a circle with radius is given by
- Area of semicircle of radius
- Area of a ring whose outer and inner radii are and respectively
- If two circles touch internally then the distance between their centres is equal to the difference of their radii
- The distance moved by a rotating wheel in one revolution is equal to the circumference of the wheel.
- The number of revolutions completed by a rotating wheel in one minute
- Length of an arc which substends an angle of at the centre
- Sector of a circle is a region enclosed by an arc of a circle and its two bounding radii.

(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.

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