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# 11X1 T07 02 angle theorems 1

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### 11X1 T07 02 angle theorems 1

1. 1. Angle Theorems
2. 2. Angle Theorems (4) The angle subtended by an arc (or chord) at the centre is double the angle subtended by the arc (or chord) at the circumference.
3. 3. Angle Theorems (4) The angle subtended by an arc (or chord) at the centre is double the angle subtended by the arc (or chord) at the circumference. C A B O
4. 4. Angle Theorems (4) The angle subtended by an arc (or chord) at the centre is double the angle subtended by the arc (or chord) at the circumference. C A B O
5. 5. Angle Theorems (4) The angle subtended by an arc (or chord) at the centre is double the angle subtended by the arc (or chord) at the circumference. C A B O
6. 6. Angle Theorems (4) The angle subtended by an arc (or chord) at the centre is double the angle subtended by the arc (or chord) at the circumference. Proof: Join BO and produce to X X C A B O
7. 7. Angle Theorems (4) The angle subtended by an arc (or chord) at the centre is double the angle subtended by the arc (or chord) at the circumference. Proof: Join BO and produce to X X C A B O
8. 8. Angle Theorems (4) The angle subtended by an arc (or chord) at the centre is double the angle subtended by the arc (or chord) at the circumference. Proof: Join BO and produce to X X C A B O
9. 9. Angle Theorems (4) The angle subtended by an arc (or chord) at the centre is double the angle subtended by the arc (or chord) at the circumference. Proof: Join BO and produce to X X C A B O
10. 10. Angle Theorems (4) The angle subtended by an arc (or chord) at the centre is double the angle subtended by the arc (or chord) at the circumference. Proof: Join BO and produce to X X C A B O
11. 11. Angle Theorems (4) The angle subtended by an arc (or chord) at the centre is double the angle subtended by the arc (or chord) at the circumference. Proof: Join BO and produce to X X C A B O
12. 12. Angle Theorems (4) The angle subtended by an arc (or chord) at the centre is double the angle subtended by the arc (or chord) at the circumference. Proof: Join BO and produce to X X C A B O
13. 13. (5a) The angle in a semicircle is a right angle.
14. 14. (5a) The angle in a semicircle is a right angle. A B O C
15. 15. (5a) The angle in a semicircle is a right angle. A B O C
16. 16. (5a) The angle in a semicircle is a right angle. A B O C
17. 17. (5a) The angle in a semicircle is a right angle. A B O C
18. 18. (5a) The angle in a semicircle is a right angle. Proof: A B O C
19. 19. (5a) The angle in a semicircle is a right angle. Proof: A B O C
20. 20. (5a) The angle in a semicircle is a right angle. Proof: A B O C
21. 21. (5a) The angle in a semicircle is a right angle. Proof: Exercise 9B; 1 ace etc, 2, 6, 8ac, 9ab, 10ac, 11ac, 12, 13 A B O C