1. Circles

2. Points & Circle Relationships Inside the circle THE circle Outside the circle A C B E G F D

3. Parts of a Circle Center Radius Diameter Chord Is a diameter a chord? P A B R C D

4. Parts of a Circle Center: P Radius: PR Diameter: AB Chord: CD & AB Is a diameter a chord? YES P A B R C D

5. Construct a Regular Hexagon 1. With a compass – make a circle 2. DO NOT CHANGE compass measure

6. Construct a Regular Hexagon 3. Place point of compass on the circle

7. Construct a Regular Hexagon 4. Make an arc to the left and right side of the compass on the circle

8. Construct a Regular Hexagon 5. Move compass to arcs and repeat 4 & 5 until you have 6 marks

9. Construct a Regular Hexagon 6. Connect the consecutive marks

10. Major & Minor Arcs An Arc is part of a circle. Minor Arc is less than half Major Arc is more than half Identify the Minor Arcs and The Major Arcs… A C B E

11. Major & Minor Arcs Identify the Minor Arcs and The Major Arcs… Minor Arcs: AB, BC, AC Major Arcs: ABC, BCA, BAC A C B   E

12. Semicircles An arc that is exactly half the circle. D F E

13. Measure of Arc Arcs are measured in two ways Degrees Length

14. Arc Measure: Degrees The arc measure corresponds the the central angle. What is the mAB? A C B 120  95   P

15. Arc Measure: Degrees What is the mAB? A C B 120  95   P

16. Arc Measure: Degrees What is the mAB? 120 A C B 95   P

17. Arc Measure: Degrees What is the mAB? 120 What is the mBC? A C B 120  95    P

18. Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 A C B 120  95    P

19. Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 What is the mAC? A C B 120  95     P

20. Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 What is the mAC? 145 A C B 120  95     P

21. Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 What is the mAC? 145 What is the mACB? A C B 120  95      P

22. Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 What is the mAC? 145 What is the mACB? 240 A C B 120  95      P

23. Arc Measure: Length The length is part of the circumference… so you would have to know the radius. A C B 120  95  P

24. Arc Measure: Length The length is part of the circumference… so you would have to know the radius. And the formula Length = 2r A C B 120  95  5cm degree    P

25. Arc Measure: Length Length = 2r AB = A C B 120  95  5cm degree     P

26. Arc Measure: Length Length = 2r AB = 25(120/360) A C B 120  95  5cm degree     P

27. Arc Measure: Length Length = 2r AB = 25(120/360) = 10.47 cm A C B 120  95  5cm degree     P

28. Arc Measure: Length Length = 2r AC = A C B 120  95  5cm degree     P

29. Arc Measure: Length Length = 2r AC = 25(145/360) A C B 120  95  5cm degree     P

30. Arc Measure: Length Length = 2r AC = 25(145/360) = 12.65 cm A C B 120  95  5cm degree     P

31. Chords and Arcs Theorem What would you think if 2 chords of a circle had equal length? A CD B P

32. Chords and Arcs Theorem What would you think if 2 chords of a circle had equal length? A CD B P AC  BD ? 

33. Chords and Arcs Theorem What would you think if 2 chords of a circle had equal length? A CD B P AC  BD ? Prove it! 

34. Chords and Arcs Theorem Draw lines to each point What do you know about the dotted lines? A CD B P

35. Chords and Arcs Theorem AP  BP (radii of the same O are  CP  DP A CD B P

36. Chords and Arcs Theorem AP  BP (radii of the same O are  CP  DP A CD B P What do you know about the triangles?

37. Chords and Arcs Theorem The  ‘s are  by SSS A CD B P

38. Chords and Arcs Theorem The  ‘s are  by SSS A CD B P So where does this lead…

39. Chords and Arcs Theorem What do you know about angles 1 & 2? A CD B P 12

40. Chords and Arcs Theorem What do you know about angles 1 & 2? A CD B P 12 <1  <2 by CPCTC

41. Chords and Arcs Theorem So the Central angles are  And the arcs formed are  A CD B P