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Friday, January 25, 2013                           AIRIL AHMAD
Friday, January 25, 2013                             CIRCLES                                 BY                           ...
Friday, January 25, 2013        CIRCLE        CIRCUMFERENCE      MINOR SECTOR        DIAMETER           ARC        RADIUS ...
Friday, January 25, 2013       Where can you find the arc around you?                                          AIRIL BIN A...
Friday, January 25, 2013       CHORD AND ARC        1. A chord is a straight line that joins        any two points on the ...
Friday, January 25, 2013       CHORD AND ARC                           CHORD                            ARC               ...
Friday, January 25, 2013       PROPERTIES OF CHORD         1. A radius that is            perpendicular to a chord        ...
Friday, January 25, 2013       PROPERTIES OF CHORD                           5cm   X cm                                   ...
Friday, January 25, 2013       PROPERTIES OF CHORD         2. Equal chords in a circle are            equidistant from the...
Friday, January 25, 2013       PROPERTIES OF CHORD                              14 c                                   m  ...
Friday, January 25, 2013       PROPERTIES OF CHORD        3. Two chords of the same            length cut arcs of the same...
Friday, January 25, 2013       PROPERTIES OF CHORD                              14 c                                   m  ...
Friday, January 25, 2013         PYTHAGORAS’ THEOREM                                  x = 3 +4                            ...
Friday, January 25, 2013   Trigonometry          3 4 5            8 15    17          5 12 13          9 12    15         ...
Friday, January 25, 2013       Example 1:                           P                                              From th...
Friday, January 25, 2013       Example 2:                         Given that AB=16cm and                                  ...
Friday, January 25, 2013       Example 3:                     Given that AB=30cm and                                      ...
Friday, January 25, 2013                           AIRIL BIN AHMAD
Friday, January 25, 2013                           PROPERTIES OF                              CIRCLE                      ...
Friday, January 25, 2013       PROPERTIES OF CIRCLE        1. Angle subtended at the           circumference by the same  ...
Friday, January 25, 2013       PROPERTIES OF CIRCLE                           ANGLE AT THE                           CIRCU...
Friday, January 25, 2013       PROPERTIES OF CIRCLE                                 500                                   ...
Friday, January 25, 2013         Example 1:                                       Find:                                   ...
Friday, January 25, 2013         Example 1:                                       Find:                           300     ...
Friday, January 25, 2013         Example 2:                                               Find:                           ...
Friday, January 25, 2013         Example 2:                                      Find:                                    ...
Friday, January 25, 2013         Example 2:                                      Find:                                    ...
Friday, January 25, 2013         Example 2:                                            Find:                              ...
Friday, January 25, 2013         Example 2:                                         Find:                               Z ...
Friday, January 25, 2013       Exercise        PAGE 48        EXERCISE 3.2A        NO. 1, 2 , 3        ENJOY DOING IT!!!  ...
Friday, January 25, 2013         Exercise:               1.Find   the value of x        a.                               ...
Friday, January 25, 2013         Exercise:                     1.Find   the value of x        c.                         ...
Friday, January 25, 2013                                      2.Find the value of x and y         Exercise:               ...
Friday, January 25, 2013                           AIRIL BIN AHMAD
Friday, January 25, 2013       PROPERTIES OF CIRCLE         2. An angle subtended at the        centre of a circle by an a...
Friday, January 25, 2013       PROPERTIES OF CIRCLE                           ANGLE AT THE                           CIRCU...
Friday, January 25, 2013       PROPERTIES OF CIRCLE                           350                                 X0= 350x...
Friday, January 25, 2013       PROPERTIES OF CIRCLE              520               X0                                  X0=...
Friday, January 25, 2013       Example 1:                           y0     x0= 3600-2500                                  ...
Friday, January 25, 2013       Example 2:                           y0         x0= 1800-600                               ...
Friday, January 25, 2013       Exercise        PAGE 52        EXERCISE 3.2C        NO. 1, 2 , 3        ENJOY DOING IT!!!  ...
Friday, January 25, 2013        A        A         B    B    C    C    D    D    E    E        16       24        8    24 ...
Friday, January 25, 2013       PROPERTIES OF CIRCLE       3. Angle subtended at the       circumference by the diameter   ...
Friday, January 25, 2013       PROPERTIES OF CIRCLE                           900                             1800        ...
Friday, January 25, 2013       Example 1:                                         X0 = 90 - 25                            ...
Friday, January 25, 2013       Exercise        PAGE 53        EXERCISE 3.2D        NO. 1, 2 , 3        ENJOY DOING IT!!!  ...
Friday, January 25, 2013                              CYCLIC                           QUADILATERAL                       ...
Friday, January 25, 2013                      A cyclic quadrilateral is            a quadrilateral which is inscribed in a...
Friday, January 25, 2013                           AIRIL BIN AHMAD
Friday, January 25, 2013        DEFINITION                   A cyclic quadrilateral is a                   quadrilateral w...
Friday, January 25, 2013                           a                                   b                                  ...
Friday, January 25, 2013                 a         b                                       e               f              ...
Friday, January 25, 2013          Exercise        pg 58          3.3c          1b      ,2 & 4                          ...
Friday, January 25, 2013                      Exterior angles                             and                     the corr...
Friday, January 25, 2013  If PQ is extended to M, then ∠RQM is an exterior angle.                               P         ...
Friday, January 25, 2013                                If SRM is a straight line,                               which is ...
Friday, January 25, 2013                For the exterior angle, ∠QRM.               Corresponding                  interio...
Friday, January 25, 2013         Homework          Pg  61          Ex.3.3e          1, 2, 3, 4                         ...
Friday, January 25, 2013         Homework          Pg  64          Ex.3.3g          1, 2, 3, 4                         ...
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NOTE MATH PMR CIRCLE

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NOTE MATH PMR CIRCLE

  1. 1. Friday, January 25, 2013 AIRIL AHMAD
  2. 2. Friday, January 25, 2013 CIRCLES BY MR.AIRIL AHMAD AIRIL AHMAD
  3. 3. Friday, January 25, 2013 CIRCLE CIRCUMFERENCE MINOR SECTOR DIAMETER ARC RADIUS MINOR ARC AREA OF SECTOR MAJOR ARC MAJOR SECTOR CHORD AIRIL BIN AHMAD
  4. 4. Friday, January 25, 2013 Where can you find the arc around you? AIRIL BIN AHMAD
  5. 5. Friday, January 25, 2013 CHORD AND ARC 1. A chord is a straight line that joins any two points on the circumference of a circle. 2. An arc is a curved line that joins any two points on the circumference of a circle. AIRIL BIN AHMAD
  6. 6. Friday, January 25, 2013 CHORD AND ARC CHORD ARC AIRIL BIN AHMAD
  7. 7. Friday, January 25, 2013 PROPERTIES OF CHORD 1. A radius that is perpendicular to a chord divides the chord into two equal parts. AIRIL BIN AHMAD
  8. 8. Friday, January 25, 2013 PROPERTIES OF CHORD 5cm X cm AIRIL BIN AHMAD
  9. 9. Friday, January 25, 2013 PROPERTIES OF CHORD 2. Equal chords in a circle are equidistant from the centre. AIRIL BIN AHMAD
  10. 10. Friday, January 25, 2013 PROPERTIES OF CHORD 14 c m 14 cm AIRIL BIN AHMAD
  11. 11. Friday, January 25, 2013 PROPERTIES OF CHORD 3. Two chords of the same length cut arcs of the same length. AIRIL BIN AHMAD
  12. 12. Friday, January 25, 2013 PROPERTIES OF CHORD 14 c m 14 cm AIRIL BIN AHMAD
  13. 13. Friday, January 25, 2013 PYTHAGORAS’ THEOREM x = 3 +4 2 2 3cm x cm x = 9 + 16 4cm x = 25 x =5 AIRIL BIN AHMAD
  14. 14. Friday, January 25, 2013 Trigonometry 3 4 5 8 15 17 5 12 13 9 12 15 6 8 10 10 24 26 7 24 25 12 16 20 AIRIL BIN AHMAD
  15. 15. Friday, January 25, 2013 Example 1: P From the figure find: a. AQ= …………cm b. OA= …………cm O c. OR= …………cm 3 cm d. OP= …………cm Q A 4 cm B e. QR= …………cm R AIRIL BIN AHMAD
  16. 16. Friday, January 25, 2013 Example 2: Given that AB=16cm and OQ=6cm from the P figure find: a. AQ= …………cm S b. OS= …………cm c. OP= …………cm O d. OA= …………cm 6 cm Q e. OR= …………cm A B f. QR= …………cm R AIRIL BIN AHMAD
  17. 17. Friday, January 25, 2013 Example 3: Given that AB=30cm and OC=8cm from the D figure find: a. AC= …………cm b. CB= …………cm c. OA= …………cm O d. OD= …………cm 8 cm e. OB= …………cm A B f. DC= …………cm C AIRIL BIN AHMAD
  18. 18. Friday, January 25, 2013 AIRIL BIN AHMAD
  19. 19. Friday, January 25, 2013 PROPERTIES OF CIRCLE BY MR.AIRIL AHMAD AIRIL AHMAD
  20. 20. Friday, January 25, 2013 PROPERTIES OF CIRCLE 1. Angle subtended at the circumference by the same arc are equal. AIRIL BIN AHMAD
  21. 21. Friday, January 25, 2013 PROPERTIES OF CIRCLE ANGLE AT THE CIRCUMFERENCE AIRIL BIN AHMAD
  22. 22. Friday, January 25, 2013 PROPERTIES OF CIRCLE 500 500 500 500 AIRIL BIN AHMAD
  23. 23. Friday, January 25, 2013 Example 1: Find: 600 a. x = ……….. 0 600 X0 y0 b. y0= ……….. 300 AIRIL BIN AHMAD
  24. 24. Friday, January 25, 2013 Example 1: Find: 300 0 600 a. x = ……….. y0 300 X0 600 b. y0= ……….. AIRIL BIN AHMAD
  25. 25. Friday, January 25, 2013 Example 2: Find: 35 0 a. x0= ……….. y0 b. y0= ……….. z0 500 X 0 c. z0= ……….. AIRIL BIN AHMAD
  26. 26. Friday, January 25, 2013 Example 2: Find: 350 a. x = ……….. 0 350 X0 b. y0= ……….. z0 500 y0 c. z0= ……….. AIRIL BIN AHMAD
  27. 27. Friday, January 25, 2013 Example 2: Find: 350 a. x = ……….. 0 500 y0 500 z0 X0 b. y0= ……….. 350 c. z0= ……….. AIRIL BIN AHMAD
  28. 28. Friday, January 25, 2013 Example 2: Find: 350 a. x = ……….. 0 350 y0 500 b. y0= ……….. Z0 X0 500 c. z0= ……….. AIRIL BIN AHMAD
  29. 29. Friday, January 25, 2013 Example 2: Find: Z 0 0 350 a. x = ……….. 500 500 X 0 b. y0= ……….. Z0 = 1800 – 350 - 500 c. z0= ……….. Z0 = 950 AIRIL BIN AHMAD
  30. 30. Friday, January 25, 2013 Exercise PAGE 48 EXERCISE 3.2A NO. 1, 2 , 3 ENJOY DOING IT!!! AIRIL BIN AHMAD
  31. 31. Friday, January 25, 2013 Exercise:  1.Find the value of x a. b. x0 320 200 x0 x0 AIRIL BIN AHMAD
  32. 32. Friday, January 25, 2013 Exercise:  1.Find the value of x c. d. 420 x0 260 580 360 x0 AIRIL BIN AHMAD
  33. 33. Friday, January 25, 2013 2.Find the value of x and y Exercise:  260 360 x0 AIRIL BIN AHMAD
  34. 34. Friday, January 25, 2013 AIRIL BIN AHMAD
  35. 35. Friday, January 25, 2013 PROPERTIES OF CIRCLE 2. An angle subtended at the centre of a circle by an arc is TWICE the angle subtended by the arc at the circumference. AIRIL BIN AHMAD
  36. 36. Friday, January 25, 2013 PROPERTIES OF CIRCLE ANGLE AT THE CIRCUMFERENCE ANGLE AT THE CENTRE AIRIL BIN AHMAD
  37. 37. Friday, January 25, 2013 PROPERTIES OF CIRCLE 350 X0= 350x 2 = 700 700 X0 AIRIL BIN AHMAD
  38. 38. Friday, January 25, 2013 PROPERTIES OF CIRCLE 520 X0 X0= 1040 ÷ 2 = 520 1040 AIRIL BIN AHMAD
  39. 39. Friday, January 25, 2013 Example 1: y0 x0= 3600-2500 x0= 1100 2500 y0= 1100 ÷ 2 X0 y0= 550 AIRIL BIN AHMAD
  40. 40. Friday, January 25, 2013 Example 2: y0 x0= 1800-600 x0= 1200 y0= 1200 ÷ 2 X0 y0= 600 300 300 AIRIL BIN AHMAD
  41. 41. Friday, January 25, 2013 Exercise PAGE 52 EXERCISE 3.2C NO. 1, 2 , 3 ENJOY DOING IT!!! AIRIL BIN AHMAD
  42. 42. Friday, January 25, 2013 A A B B C C D D E E 16 24 8 24 4 20 2 18 1 17 17 25 9 25 5 21 3 19 3 19 18 26 10 26 6 22 6 22 5 21 19 27 11 27 7 23 7 23 7 23 20 28 12 28 12 28 10 26 9 25 21 29 13 29 13 29 11 27 11 27 22 30 14 30 14 30 14 30 13 29 23 31 15 31 15 31 15 31 15 31 AIRIL BIN AHMAD
  43. 43. Friday, January 25, 2013 PROPERTIES OF CIRCLE 3. Angle subtended at the circumference by the diameter of a semicircle = 900 AIRIL BIN AHMAD
  44. 44. Friday, January 25, 2013 PROPERTIES OF CIRCLE 900 1800 AIRIL BIN AHMAD
  45. 45. Friday, January 25, 2013 Example 1: X0 = 90 - 25 X0 = 650 900 x0 25 0 y0 = 90 - 38 380 y0 y0 = 520 900 AIRIL BIN AHMAD
  46. 46. Friday, January 25, 2013 Exercise PAGE 53 EXERCISE 3.2D NO. 1, 2 , 3 ENJOY DOING IT!!! AIRIL BIN AHMAD
  47. 47. Friday, January 25, 2013 CYCLIC QUADILATERAL BY MR.AIRIL AHMAD AIRIL AHMAD
  48. 48. Friday, January 25, 2013 A cyclic quadrilateral is a quadrilateral which is inscribed in a circle. P Q S R PQRS is a cyclic quadrilateral. AIRIL BIN AHMAD
  49. 49. Friday, January 25, 2013 AIRIL BIN AHMAD
  50. 50. Friday, January 25, 2013 DEFINITION A cyclic quadrilateral is a quadrilateral with its four vertices located on the circumference of a circle AIRIL BIN AHMAD
  51. 51. Friday, January 25, 2013 a b a + c = 1800 b + d = 1800 d c AIRIL BIN AHMAD
  52. 52. Friday, January 25, 2013 a b e f d c h g j k q n m r t s AIRIL BIN AHMAD
  53. 53. Friday, January 25, 2013  Exercise pg 58  3.3c  1b ,2 & 4 AIRIL BIN AHMAD
  54. 54. Friday, January 25, 2013 Exterior angles and the corresponding interior angles AIRIL BIN AHMAD
  55. 55. Friday, January 25, 2013 If PQ is extended to M, then ∠RQM is an exterior angle. P Q M S R AIRIL BIN AHMAD
  56. 56. Friday, January 25, 2013 If SRM is a straight line, which is the exterior angle? P Q S ∠QRM is the exterior angle. R M AIRIL BIN AHMAD
  57. 57. Friday, January 25, 2013 For the exterior angle, ∠QRM. Corresponding interior P opposite angle Q S R 650 Exterior angle Corresponding interior angle M AIRIL BIN AHMAD
  58. 58. Friday, January 25, 2013 Homework  Pg 61  Ex.3.3e  1, 2, 3, 4 AIRIL BIN AHMAD
  59. 59. Friday, January 25, 2013 Homework  Pg 64  Ex.3.3g  1, 2, 3, 4 AIRIL BIN AHMAD

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