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Circle

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Circle

  1. 1. MATHEMATICS STANDARD : VI Bombay Cambridge Gurukul Bombay Cambridge Gurukul 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. BACK
  8. 8. The distance around a circle is called its circumference. O Centre Circumference A circle A BACK
  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. BACK 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…) BACK
  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…) BACK
  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 BACK
  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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