Circle

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Circle

  1. 1. MATHEMATICS STANDARD : VI Circle
  2. 2. Contents Circle in daily life Circle in music Circle in sports Circle Centre Circumference Circular region Radius Diameter Chord Arc Semicircle Segments of a circle Crossword S Radius OM Centre M Chord PQ P E D Q G Arc RE O F Diameter DE
  3. 3. CIRCLE IN DAILY LIFE A circle BACK
  4. 4. CIRCLE IN MUSIC BACK Many musical instruments have a circular surface. For example: Bingo Drum Tabla Snare Drum Bass Drum
  5. 5. CIRCLE IN SPORTS Five rings in the logo of Olympic games BACK A circle
  6. 6. A circle can be drawn with the help of a circular object. For example: A circle drawn with the help of a coin. A circle is a closed curve in a plane. What is a Circle? BACK
  7. 7. This fixed point (equidistant) inside a circle is called centre. Circle and Centre of a circle A circle is a closed curve consisting of all points in a plane which are at the same distance (equidistant) from a fixed point inside it. O Centre A circle A circle has one and only one centre.
  8. 8. The distance around a circle is called its circumference. O Centre Circumference A circle A
  9. 9. Circular Region A circle divides a plane into three parts. 2. Interior of a circle 3. Exterior of a circle A plane The interior of a circle together with its circumference is called the circular region. O Centre 1. The circle
  10. 10. Radius A line segment that joins any point on the circle to its centre is called a radius. M A point on the circle Radius (Contd…) Centre O
  11. 11. <ul><li>Radii ( plural of radius ) of a circle are equal in length . </li></ul><ul><li>Infinite number of radius can be drawn in a circle. </li></ul>Radius Centre K O L M N (Contd…)
  12. 12. Diameter AB A line segment that joins any two points on the circle and passes through its centre is called a diameter . A B A circle Diameter (Contd…) O Centre
  13. 13. A circle O M <ul><li>Infinite number of diameters can be drawn in a circle. </li></ul><ul><li>As the radii of a circle are equal in length, its diameters too </li></ul><ul><li>are equal in length. </li></ul>B Q (Contd…) P A N Centre
  14. 14. The length of the diameter of a circle is twice the length of its radius. Radius OM Centre M O N Radius ON Diameter MN Diameter MN = Radius OM + Radius ON Radius OM = Radius ON (Contd…)
  15. 15. Chord A line segment that joins any two points on the circle is called a chord . O B A A is a point on the circle B is another point on the circle A line segment that joins point A and B Chord
  16. 16. Diameter is also a chord of the circle. O Chord CD C D M N K L Chord MN Chord KL (Contd…) Diameter CD
  17. 17. The diameter is the longest chord . O Diameter CD C D M N Chord MN (Contd…) C D M N Chord KL L K
  18. 18. L K M N Chord MN Infinite number of chords can be drawn in a circle. Chord KL Chord GH G H BACK O Centre
  19. 19. Arc An arc is the distance between any two points on the circumference of a circle. Arc (Contd…) O Centre K L
  20. 20. An arc is named by three points , of which two are the end points of the arc and the third one lies in between them. Naming an arc (Contd…) Arc KXL O Centre L K X
  21. 21. X An arc divides the circle into two parts: the smaller arc is called the minor arc , the larger one is called the major arc . (Contd…) O Centre L K Y Minor Arc KXL Major Arc KYL
  22. 22. Example of an arc An arc An arc
  23. 23. <ul><li>Half of a circle is called a semicircle. </li></ul>Centre O Diameter D E Semicircle S <ul><li>A semicircle is also an arc of the circle. </li></ul>R (Contd…) Arc DSE Semicircle DRE Semicircle DSE Arc DRE
  24. 24. E Diameter Semicircular region Semicircular region The diameter of a circle divides it into 2 semicircular regions. D BACK Centre O Semicircle DSE Semicircle DRE
  25. 25. Segments of a Circle A chord divides the circular region into 2 parts , each of which is called a segment of the circle. Centre O D E Chord DE Minor segment of a circle Major segment of a circle S R (Contd…)
  26. 26. D E Chord DE Minor segment of the circle Major segment of the circle P Q <ul><li>The part of the circular region enclosed by a minor arc and </li></ul><ul><li>the chord is called a minor segment. </li></ul><ul><li>Minor segment does not contain the centre of the circle. </li></ul><ul><li>The part of the circular region enclosed by a major arc and </li></ul><ul><li>the chord is called a major segment. </li></ul><ul><li>Major segment contains the centre of the circle. </li></ul>BACK Centre O Minor arc DPE Major arc DQE
  27. 27. Radius Diameter Chord Arc Semi Circle Centre O Recap the Terms
  28. 28. Radius Diameter Chord Arc Semi Circle Radius OM Centre M O
  29. 29. Radius Diameter Chord Arc Semi Circle Centre E D Diameter DE O
  30. 30. Radius Diameter Chord Arc Semi Circle Centre Chord PQ P Q O
  31. 31. Radius Diameter Chord Arc Semi Circle Centre E G O F Arc PQR
  32. 32. Radius Diameter Chord Arc Semi circle S Centre O Diameter Semicircle D E Semicircle Semicircle DSE
  33. 33. C 2 C U M F E R N C E A E I Down 1. The distance between any two points on the circumference of the circle. 2. The distance around the circle. 3. The distance from the centre of the circle to a point on the circle. R D I U S R 1 C 3 R A Across: 4. The line segment that joins any two points on the circle and passes through its centre. 5. A closed curve in a plane. 6. All points on the circle are equidistant from this point. 7. A line segment that joins any two points on a circle. 4 D A M T E E 5 I R L E 6 C E N T E H R O D 7 Circle Crossword
  34. 34. Created by The Department of Research Bombay Cambridge Gurukul The End

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