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- 1. Circle Geometry
- 2. Circle Geometry Circle Geometry Definitions
- 3. Circle Geometry Circle Geometry Definitions
- 4. Circle Geometry Circle Geometry Definitions Radius: an interval joining centre to the circumference radius
- 5. Circle Geometry Circle Geometry Definitions Radius: an interval joining centre to the circumference radius Diameter: an interval passing through the centre, joining any two points on the circumference diameter
- 6. Circle Geometry Circle Geometry Definitions Radius: an interval joining centre to the circumference radius Diameter: an interval passing through the centre, joining any two points on the circumference diameter Chord: an interval joining two points on the circumference chord
- 7. Circle Geometry Circle Geometry Definitions Radius: an interval joining centre to the circumference radius Diameter: an interval passing through the centre, joining any two points on the circumference diameter Chord: an interval joining two points on the circumference chord Secant: a line that cuts the circle secant
- 8. Circle Geometry Circle Geometry Definitions Radius: an interval joining centre to the circumference radius Diameter: an interval passing through the centre, joining any two points on the circumference diameter Chord: an interval joining two points on the circumference chord Secant: a line that cuts the circle secant Tangent: a line that touches the circle tangent
- 9. Circle Geometry Circle Geometry Definitions Radius: an interval joining centre to the circumference radius Diameter: an interval passing through the centre, joining any two points on the circumference diameter Chord: an interval joining two points on the circumference chord Secant: a line that cuts the circle secant Tangent: a line that touches the circle tangent Arc: a piece of the circumference arc
- 11. Sector: a plane figure with two radii and an arc as boundaries. sector
- 12. Sector: a plane figure with two radii and an arc as boundaries. sector The minor sector is the small “piece of the pie”, the major sector is the large “piece”
- 13. Sector: a plane figure with two radii and an arc as boundaries. sector The minor sector is the small “piece of the pie”, the major sector is the large “piece” A quadrant is a sector where the angle at the centre is 90 degrees
- 14. Sector: a plane figure with two radii and an arc as boundaries. sector The minor sector is the small “piece of the pie”, the major sector is the large “piece” A quadrant is a sector where the angle at the centre is 90 degrees Segment: a plane figure with a chord and an arc as boundaries. segment
- 15. Sector: a plane figure with two radii and an arc as boundaries. sector The minor sector is the small “piece of the pie”, the major sector is the large “piece” A quadrant is a sector where the angle at the centre is 90 degrees Segment: a plane figure with a chord and an arc as boundaries. segment A semicircle is a segment where the chord is the diameter, it is also a sector as the diameter is two radii.
- 17. Concyclic Points: points that lie on the same circle. A B C D
- 18. Concyclic Points: points that lie on the same circle. concyclic points A B C D
- 19. Concyclic Points: points that lie on the same circle. concyclic points Cyclic Quadrilateral: a four sided shape with all vertices on the same circle. cyclic quadrilateral A B C D
- 21. A B
- 22. A B represents the angle subtended at the centre by the arc AB
- 23. A B represents the angle subtended at the centre by the arc AB
- 24. A B represents the angle subtended at the centre by the arc AB represents the angle subtended at the circumference by the arc AB
- 25. A B represents the angle subtended at the centre by the arc AB represents the angle subtended at the circumference by the arc AB
- 26. A B represents the angle subtended at the centre by the arc AB represents the angle subtended at the circumference by the arc AB Concentric circles have the same centre.
- 29. Circles touching internally share a common tangent.
- 30. Circles touching internally share a common tangent. Circles touching externally share a common tangent.
- 31. Circles touching internally share a common tangent. Circles touching externally share a common tangent.
- 32. Circles touching internally share a common tangent. Circles touching externally share a common tangent.
- 33. Chord (Arc) Theorems
- 34. Chord (Arc) Theorems Note: = chords cut off = arcs
- 35. Chord (Arc) Theorems Note: = chords cut off = arcs (1) A perpendicular drawn to a chord from the centre of a circle bisects the chord, and the perpendicular bisector of a chord passes through the centre.
- 36. Chord (Arc) Theorems Note: = chords cut off = arcs (1) A perpendicular drawn to a chord from the centre of a circle bisects the chord, and the perpendicular bisector of a chord passes through the centre. A B O X
- 37. Chord (Arc) Theorems Note: = chords cut off = arcs (1) A perpendicular drawn to a chord from the centre of a circle bisects the chord, and the perpendicular bisector of a chord passes through the centre. A B O X
- 38. Chord (Arc) Theorems Note: = chords cut off = arcs (1) A perpendicular drawn to a chord from the centre of a circle bisects the chord, and the perpendicular bisector of a chord passes through the centre. A B O X
- 39. Chord (Arc) Theorems Note: = chords cut off = arcs (1) A perpendicular drawn to a chord from the centre of a circle bisects the chord, and the perpendicular bisector of a chord passes through the centre. A B O X
- 40. Chord (Arc) Theorems Note: = chords cut off = arcs (1) A perpendicular drawn to a chord from the centre of a circle bisects the chord, and the perpendicular bisector of a chord passes through the centre. Proof: Join OA , OB A B O X
- 41. Chord (Arc) Theorems Note: = chords cut off = arcs (1) A perpendicular drawn to a chord from the centre of a circle bisects the chord, and the perpendicular bisector of a chord passes through the centre. Proof: Join OA , OB A B O X
- 42. Chord (Arc) Theorems Note: = chords cut off = arcs (1) A perpendicular drawn to a chord from the centre of a circle bisects the chord, and the perpendicular bisector of a chord passes through the centre. Proof: Join OA , OB A B O X
- 43. Chord (Arc) Theorems Note: = chords cut off = arcs (1) A perpendicular drawn to a chord from the centre of a circle bisects the chord, and the perpendicular bisector of a chord passes through the centre. Proof: Join OA , OB A B O X
- 44. Chord (Arc) Theorems Note: = chords cut off = arcs (1) A perpendicular drawn to a chord from the centre of a circle bisects the chord, and the perpendicular bisector of a chord passes through the centre. Proof: Join OA , OB A B O X
- 45. Chord (Arc) Theorems Note: = chords cut off = arcs (1) A perpendicular drawn to a chord from the centre of a circle bisects the chord, and the perpendicular bisector of a chord passes through the centre. Proof: Join OA , OB A B O X
- 46. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles.
- 47. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. A B O X
- 48. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. A B O X
- 49. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. A B O X
- 50. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. A B O X
- 51. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. Proof: Join OA , OB A B O X
- 52. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. Proof: Join OA , OB A B O X
- 53. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. Proof: Join OA , OB A B O X
- 54. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. Proof: Join OA , OB A B O X
- 55. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. Proof: Join OA , OB A B O X
- 56. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. Proof: Join OA , OB A B O X
- 57. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. Proof: Join OA , OB A B O X
- 58. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. Proof: Join OA , OB A B O X
- 59. (2) Converse of (1) The line from the centre of a circle to the midpoint of the chord at right angles. Proof: Join OA , OB A B O X
- 60. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre.
- 61. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. A B O X C D Y
- 62. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. A B O X C D Y
- 63. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. A B O X C D Y
- 64. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. A B O X C D Y
- 65. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. A B O X C D Y
- 66. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. Proof: Join OA , OC A B O X C D Y
- 67. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. Proof: Join OA , OC A B O X C D Y
- 68. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. Proof: Join OA , OC A B O X C D Y
- 69. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. Proof: Join OA , OC A B O X C D Y
- 70. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. Proof: Join OA , OC A B O X C D Y
- 71. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. Proof: Join OA , OC A B O X C D Y
- 72. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. Proof: Join OA , OC A B O X C D Y
- 73. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. Proof: Join OA , OC A B O X C D Y
- 74. (3) Equal chords of a circle are the same distance from the centre and subtend equal angles at the centre. Proof: Join OA , OC A B O X C D Y
- 75. A B O C D
- 76. A B O C D
- 77. A B O C D
- 78. Proof: A B O C D
- 79. Proof: A B O C D
- 80. Proof: A B O C D
- 81. Proof: A B O C D
- 82. Proof: Exercise 9A; 1 ce, 2 aceg, 3, 4, 9, 10 ac, 11 ac, 13, 15, 16, 18 A B O C D

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