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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