1. © T Madas O O O O O O O The Circle Theorems

2. © T Madas 1 st Theorem

3. © T Madas The perpendicular bisector of a chord passes through the centre of the circle O

4. O The perpendicular bisector of a chord passes through the centre of the circle

5. © T Madas O The perpendicular bisector of a chord passes through the centre of the circle

6. © T Madas Finding the Centre of Rotation

7. The shapes below have been produced by rotation. Find the centre of rotation Why does it work?

8. © T Madas The shapes below have been produced by rotation. Find the centre of rotation

9. © T Madas The shapes below have been produced by rotation. Find the centre of rotation

10. © T Madas The shapes below have been produced by rotation. Find the centre of rotation

11. © T Madas 2 nd Theorem

12. © T Madas O Inscribed angles which correspond to the same arc are equal Inscribed Angle

13. © T Madas O Inscribed angles which correspond to the same arc are equal Does this inscribed angle correspond to the same arc?

14. © T Madas 3 rd Theorem

15. © T Madas A central angle is twice as large as any inscribed angle which corresponds to the same arc Central Angle Inscribed Angle O

16. © T Madas Various Forms of the Theorem O O O O O

17. © T Madas 4 th Theorem

18. © T Madas O An inscribed angle which corresponds to a diameter ( or semicircle ) is a right angle

19. 5 th Theorem

20. © T Madas O Cyclic Quadrilateral Opposite angles in a cyclic quadrilateral are supplementary

21. © T Madas 6 th Theorem

22. © T Madas O Tangent Tangent point A tangent and a radius drawn at any point on the circumference of the circle meet at right angles

23. © T Madas 7 th Theorem

24. © T Madas O The intersection of two tangents to a circle is equidistant from their points of contact. [Their angle of intersection and the central angle formed by the radii at the points of contact, are supplementary]

25. 8 th Theorem

26. © T Madas O segment sector segment

27. © T Madas O Alternating Segments

28. © T Madas O The angle formed by a chord and a tangent at one of its endpoints is equal to the inscribed angle corresponding to the same chord in the alternating segment

29. Circle Theorem Test

30. Circle Theorem Mini Test

32. Practice Question 1

33. © T Madas O 30° x 45° 30° 15° 150° 15°

34. © T Madas Practice Question 2

35. © T Madas 50° z 100° 50° 30° x y O

36. © T Madas Practice Question 3

37. © T Madas 70° a b c 20° 70° 20° O

38. © T Madas Practice Question 4

39. © T Madas 95° n m 55° 85° 40° p 55° O

40. © T Madas Practice Question 5

41. © T Madas 25° x y Tangent point 65° O

42. © T Madas Practice Question 6

43. © T Madas 55° s t 110° O

44. © T Madas Practice Question 7

45. © T Madas u 28° v 56° O

46. © T Madas Practice Question 8

47. © T Madas 300° h O 60° 30° 150°

48. © T Madas Practice Question 9

49. © T Madas 130° c 50° 100° O

50. © T Madas Practice Question 10

51. © T Madas 50° a b 25° O

52. © T Madas 50° a b 130° 25° Can you solve this problem without a circle theorem? O

53. © T Madas Practice Question 11

54. © T Madas 65° x 230° 115° O

55. © T Madas Practice Question 12

56. © T Madas 100° z 200° O

57. © T Madas Practice Question 13

58. © T Madas 84° a b O 42° 138°

59. © T Madas Practice Question 14

60. © T Madas 32° g O f 148° 32° 64° 296°

61. © T Madas Practice Question 15

62. © T Madas 115° p O q 65° 90° 25°

63. © T Madas Practice Question 16

64. © T Madas 90° x O 45°

65. © T Madas Practice Question 17

66. © T Madas 70° p O A B C AB = BC q r 55° 90° 35° 20°

67. © T Madas Practice Question 18

68. © T Madas 72° u O v 90° 18° 72°

69. © T Madas Practice Question 19

70. © T Madas 30° a O b c Tangent point 60° 120°

71. © T Madas Practice Question 20

72. © T Madas O 58° z y x 32° 58°

73. © T Madas Practice Question 21

74. © T Madas 85° x O 95° 85°

75. © T Madas Practice Question 22

76. © T Madas 57° t O r 123° 57° Can you think of another reason as to why both these angles are 57° ?

77. © T Madas Practice Question 23

78. © T Madas 56° 62° w O x y z 124° 56° 62° 118°

79. © T Madas Practice Question 24

80. © T Madas u 45° 160° 155° O 25° 20° 25° 135° v 20°

81. © T Madas Practice Question 25

82. © T Madas 30° x O 120° 240°

83. © T Madas Practice Question 26

84. © T Madas 75° O x 30° 60°

85. © T Madas Practice Question 27

86. © T Madas 72° x O 144° 18°

87. © T Madas Practice Question 28

88. © T Madas 40° a O b 140° 50°

89. © T Madas Practice Question 29

90. © T Madas 30° θ O 60° 30°

91. © T Madas Practice Question 30

92. © T Madas 25° n O 65°

93. © T Madas Practice Question 31

94. © T Madas O a 22° b c d Tangent point 22° 68° 56° 124° 68° Exam question

95. © T Madas