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

3. Content

4. Main Menu Review Angle in semi-circle Angle in the same segment Exercise

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

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

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

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

9. Given that AC = 6 and BC = 8. Find the radius of the circle. Solutions: AB 2 = AC 2 + BC 2 = 6 2 + 8 2 AB= 10 ( the converse of  in semi-circle ) AB C 68 Since  BCA = 90 , AB is a diameter.  radius = 10  2 = 5 Content Previous page

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

11. A B C’ C We try to rotate the  ABC’ the  ABC’ C’ Content Next page Previous page

12. A B C’ C O  AOB = 2 22 2 ACB (  at centre twice  at circumference)  AOB = 2 22 2 AC’B   ACB=  AC’B O is the centre of circle Content Next page Previous page

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

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

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

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

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

18. 30  x Find x. 40  55  50  30  70  100  Exercise Three C A E B D

19. 60  x Find x. 60  50  45  65  100  140  Exercise Four E A C D B

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

21. Exercises Wrong!! Try Again

22. Exercises Wrong!! Try Again

23. Exercises Wrong!! Try Again

24. Exercises Wrong!! Try Again

25. Exercises Correct !!

26. 35  x Exercise One Find x. 90  55  45  65  35  Exercises A B C D E

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

28. 30  x Find x. 40  55  50  30  70  100  Exercise Three Exercises A B C D E

29. 60  x Find x. 60  50  45  65  100  140  Exercise Four Exercises A B C D E

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