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Yu Chun Keung Memorial College No.2

Yu Chun Keung Memorial College No.2. F. 4 Mathematics Angles in a Circle. Chan K.B.(T1). Angles in a Circle. Content. Angles in a Circle. Content. Review. Angle in semi-circle. Angle in the same segment. Exercise. Main Menu. a. O. b. Review.

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Yu Chun Keung Memorial College No.2

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  1. Yu Chun Keung Memorial College No.2 F. 4 Mathematics Angles in a Circle Chan K.B.(T1)

  2. Angles in a Circle Content

  3. Angles in a Circle Content Review Angle in semi-circle Angle in the same segment Exercise Main Menu

  4. a O b Review What is the relationship between the a and b? Hint : O is the centre. b = 2a at centre twice  at circumference Content

  5. C A B O Angle in Semi-circle Given: In a circle , O is centre. diameter AB is AOB = 180o 90o ACB = Next page Content

  6. 90 90 75 75 105 105 60 60 120 120 C 45 45 135 135 C’ Protractor Protractor 30 30 150 150 15 15 165 165 Made in China Made in China 0 0 180 180 B A O ACB = AC ’B=90o Next page Previous page Content

  7. C 30 A B Example 1 AB is a diameter. Find CAB. Solutions: BCA = 90 (  in semi-circle ) CAB + ABC + BCA = 180 ( s sum of  ) CAB + 30 + 90 = 180  CAB = 60 Next page Previous page Content

  8. C 6 8 A B Example 2 Given that AC = 6 and BC = 8. Find the radius of the circle. Solutions: Since BCA = 90, AB is a diameter. ( the converse of  in semi-circle ) AB2 = AC2 + BC2 = 62 + 82 AB = 10  radius = 10  2 = 5 Content Previous page

  9. C C’ B A Angles in same Segment Given: AB is not a diameter, just a chord. IsACB = AC’B ? Next page Content

  10. C C’ C’ C’ C’ C’ C’ C’ C’ C’ C’ C’ C’ B A We try to rotate the DABC’ Next page Previous page Content

  11. C C’ O B A Proof O is the centre of circle AOB = 2 ACB AOB = 2 AC’B (at centre twice  at circumference)  ACB= AC’B Next page Previous page Content

  12. Q R x 95 T 40 P S Example 3 Find x. Solutions: PQT = 180QTPTPQ (  sum of  ) = 1809540 = 45 Besides,x = PQT (  in same segment ) = 45 Next page Previous page Content

  13. Q R 45 T 55 y P S Example 4 Given that TP = TS. Find y. Solutions: QPR = QSR = 55. (  in same segment ) Since TP = TS, TPS = TSP = y.  TPS +  TSP + QPT + SQP = 180 (  sum of  ) y + y + 55 + 45 = 180 2y = 80 Content y = 40 Previous page

  14. Exercises Question 1 Ans 1 Work Harder Ans 2 Question 2 Ans 3 Question 3 Ans 4 Question 4 Ans 5 Question 5 Content

  15. Exercise One Find x . A 90 35 B 55 C 45 x D 65  E 35

  16. Exercise Two AB=8 and Radius=5. Find x . B A 6 8 A B 4 x 5 C 8 C D 5 E 10

  17. Exercise Three Find x . A 40 x 100 B 55 30 C 50 D 30 E 70

  18. Exercise Four Find x . A 60 60 B 50 x C 45 140 D 65  E 100

  19. Exercise Five Find x . A 90 B 55 40 C 45 x D 50  E 40

  20. Wrong!! Try Again Exercises

  21. Wrong!! Try Again Exercises

  22. Wrong!! Try Again Exercises

  23. Wrong!! Try Again Exercises

  24. Correct !! Exercises

  25. Exercise One Find x . 90 35 55 45 x 65  35 Exercises

  26. Exercise Two AB=8 and Radius=5. Find x . B 6 8 A 4 x 5 8 C 5 10 Exercises

  27. Exercise Three Find x . 40 x 100 55 30 50 30 70 Exercises

  28. Exercise Four Find x . 60 60 50 x 45 140 65  100 Exercises

  29. Exercise Five Find x . 90 55 40 45 x 50  40 Exercises

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