1. Geometry 6 Level 1

2. Parts of a circle

3. Why is this triangle isosceles?

4. Two sides are radii

5. Find the value of x 35 x

6. Find the value of x 60 x

7. Find the value of x x

8. x 20

9. Reminder: Exterior angle equals the sum of the opposite interior angles.

10. Find the value of x. 70 50 x

11. Let’s investigate

12. We now have two isosceles triangles

13. In each case their base angles are equal.

14. The exterior angle is twice the opposite internal angle

16. The angle at the centre is twice the angle at the circumference

17.  at centre 2x2x x

19. Find the value of x x 50

20. Find the value of x x 160

21. Find the value of x x 90

22. Find the value of x x 60

23. Another way of looking at this. 2x2x x

24. Find the value of x. 240 x

25. Find the value of x. 110 x

26. Find the value of x. 135 x

27. Notice if AC is a diameter 2x2x x x

28. Find the value of x. 55 x

29. Find the value of x. 80 x

30. Find the value of x. 140 x

31. Find the value of x. 50 x

32. Find the value of x. 74 x 62

33. Find the value of x. 74 x 62

34. Find the value of x x 75

35. Find the value of y y 75 75

36. Find the value of z z 75 75

37. Angles on the same arc are the same.

40. Angles same arc

43. Why is it important?

46. Find A, B and C

47. If BC is a diameter… x x 2x2x

48. x x 2x2x y y 2y2y

49. x x 2x2x y y 2y2y

50. x x 2x2x y y 2y2y

52.  in a semi-circle

53. If AC is a diameter, find the value of x. 50 x

54. If AC is a diameter, find the value of x. 50 x

55. If AC is a diameter, find the value of x 40 x

56. 2x2x x 360 - 2x 180 - x

57. x

58. Cyclic Quadrilateral Opposite angles in a cyclic quadrilateral sum to 180 degrees. Web animation Cyclic quadrilateral

59. Opposite angles add up to 180 in a cyclic quadrilateral

60. Find the value of x x 120

61. Find the value of angles A and B.

62. 110 A B

63. PQ is a diameter.  RPQ = 30. Find  RSP.

65. Chord

66. If a diameter cuts a chord in half, it form a right angle.

67. Tangent

68. Tgt rad A radius is always perpendicular to a tangent at the point of contact.

69. Find the values of x, y and z 72 x y z

70. Find the values of x, y and z 72 x y z

71. Find the values of x, y and z 72 x y z Tgt. — rad  In semi-circle  ’s ∆

72. Notice z 72 x y z

73. Notice z 72 x y z z

74. Exterior angle at a tangent always equals the opposite interior angle. 72 z

75. Find the values of angles x and y. 62 x y 71

76. Find the angle ACB.

77. Find the value of x. x 128 x 42

78. Find the value of x. x = 52 128 x =69 42

79. Find the value of x

80. Find, in terms of x,  ADB,  AOD.  ABD

81.  ADB = 2 x,  AOD = 180 - 6 x,  ABD = 90 - 3 x

82. If the angle PCQ = 72, what is the reflex angle POQ ? 252

83. Find the angle ABC 112

84. a) Calculate the angle between the tangent and the line AC. b) Calculate the angle ABC.

85. Determine the angle QAC in terms of x. Calculate the value of x..

86. Determine the angle QAC. Calculate the value of x.. 75

87. a) Work out the following angles: i) ACD ii) BCA iii) CDA b) Show that the triangle EBA is isosceles.

88. ABC and ADE are straight lines. The diameter of the larger circle is CE.

89. Express in terms of x, the following angles: a) ABD b) BDC c) BAD