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# 10.1 Angles in Circles

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### 10.1 Angles in Circles

1. 1. 10.1 Angles in Circles 1 March 24, 2014 Circle Geometry 10.1 Exploring Angles in a Circle
2. 2. 10.1 Angles in Circles 2 March 24, 2014 Anatomy of a Circle What do we know about a circle?
3. 3. 10.1 Angles in Circles 3 March 24, 2014 Anatomy of a Circle Chord: A line segment with both endpoints on a circle
4. 4. 10.1 Angles in Circles 4 March 24, 2014 Anatomy of a Circle Central Angle: An angle formed by two radii of a circle.
5. 5. 10.1 Angles in Circles 5 March 24, 2014 Anatomy of a Circle Inscribed Angle: An angle formed by two chords that share a common endpoint
6. 6. 10.1 Angles in Circles 6 March 24, 2014 Anatomy of a Circle Arc (of a circle): A portion of the circumference
7. 7. 10.1 Angles in Circles 7 March 24, 2014 Properties of Angles The inscribed angles subtended by the same arc are congruent.
8. 8. 10.1 Angles in Circles 8 March 24, 2014 Tips and Tricks If you see a bow tie, you have sets of inscribed angles.
9. 9. 10.1 Angles in Circles 9 March 24, 2014 Properties of Angles The measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc. B A C O
10. 10. 10.1 Angles in Circles 10 March 24, 2014 Tips and Tricks If you see a Star Trek insignia, you have a set of inscribed angles and central angles.
11. 11. 10.1 Angles in Circles 11 March 24, 2014 Example Find ∠ACD and ∠AOD if ∠ABD is 35˚
12. 12. 10.1 Angles in Circles 12 March 24, 2014 Example Find ∠ACD and ∠AOD if ∠ABD is 35˚
13. 13. 10.1 Angles in Circles 13 March 24, 2014 Properties of Angles Angles inscribed in a semicircle are right angles.
14. 14. 10.1 Angles in Circles 14 March 24, 2014 Example Point C is the centre of the circle. The diameter AB is 10cm and the chord BD is 6 cm. B D C A
15. 15. 10.1 Angles in Circles 15 March 24, 2014 Example Determine the measure of the missing angle
16. 16. 10.1 Angles in Circles 16 March 24, 2014 Example Determine the measure of angle y
17. 17. 10.1 Angles in Circles 17 March 24, 2014
18. 18. 10.1 Angles in Circles 18 March 24, 2014 Example Determine the measure of the missing angles
19. 19. 10.1 Angles in Circles 19 March 24, 2014 Example Determine the measure of the missing angles
20. 20. 10.1 Angles in Circles 20 March 24, 2014 Example Determine the measure of the missing angle
21. 21. 10.1 Angles in Circles 21 March 24, 2014 Questions page 382 3, 4, 10, 12, 20a