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# 11X1 T07 01 definitions & chord theorems

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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
• 10.
• 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.
• 16.
• 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
• 20.
• 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.
• 27.
• 28.
• 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