# 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 theangle subtendedat the centre by the arcAB 23. A B represents theangle subtendedat the centre by the arcAB 24. A B represents theangle subtendedat the centre by the arcAB represents theangle subtendedat the circumference by the arcAB 25. A B represents theangle subtendedat the centre by the arcAB represents theangle subtendedat the circumference by the arcAB 26. A B represents theangle subtendedat the centre by the arcAB represents theangle subtendedat the circumference by the arcAB Concentric circleshave the same centre. 27. 28. 29. Circles touching internallyshare a common tangent. 30. Circles touching internallyshare a common tangent. Circles touching externallyshare a common tangent. 31. Circles touching internallyshare a common tangent. Circles touching externallyshare a common tangent. 32. Circles touching internallyshare a common tangent. Circles touching externallyshare 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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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: JoinOA ,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