1. Circles 9.1: Parts of a Circle 9.2: Tangents 9.3: Arcs 9.4: Chords 10.8: Circumference 10.9: Arc Length 10.10: Area of a Circle 10.11: Area of a Sector/Segment Homework: 9.1: 1-11 9.2: 1-14, skip 9 9.3: ALL 9.4: 8-13, 17-22 10.8: ALL 10.9: ALL 10.10: 1-5, 11-13 10.11: 3-17

2. Essential Question: What are the important parts that make up a circle?

3. the set of all points in a plane that are at a given distance from a given point

4. center outer endpoints circle passescircle intersects intersects one tangent

5. twoone two center radii same different

8. Circle A and Circle C b/c Same radius, different center

9. Essential Question: How can you determine if a line is tangent to a circle?

10. What is a tangent? Tell your neighbor what a tangent is

11. tangent perpendicular point

12. tangent external congruent If you can prove the Two Tangents Theorem, you will win a candy prize.

13. Tangents are perpendicular to the radius a 2 + b 2 = c 2 5 2 + 8 2 = c 2 25 + 64 = c 2 89 = c 2 √ 89 ≈ 9.43= c

14. 6 4 7 6+ 6 + 4 + 4 + 7 + 7 = 34

15. Essential Question: How do you find the measure of a central angle?

16. 360 portion of the circumference of a circle half circle angle whose vertex is the center of the circle

17. less 180 greater 180 Use 3 letters to name: ex. Arc BDC

18. The measure of an arc formed by 2 adjacent arcs is the sum of the measures of the arcs Arc AD + Arc DB = Arc AB

19. Arc AB= 102° Arc ADB= 360 – 102 = 258°

20. 90° 120° 38°

21. 90° 120° 38° 120+38= 158° 90+38+120= 248° 360 – 90= 270°

22. 9.1 #1-11 9.3 ALL

23. Essential Question: How can you determine if two chords are congruent?

27. 125° 125° 125° 80° x x 360 – 80 = 280 280/2 = 140°

28. x= 6 y= 75°

29. 35 = 6x – 7 42 = 6x 7 = x Independently try…

30. 9.2 (#1 – 14, skip 9) 9.4 (#8 – 13, 17 – 22)

31. Essential Question: What is the circumference of a circle?

32. distance around a circle 2πrπd

33. C = 2π(7) =14π cm C=2πr or C=πd 64π = πd 64in=d

34. C=2πr or C=πd C=π(10) =10π in

35. Essential Question: How do you find the length of only part of the distance around a circle?

36. distance along an arc

37. PQ

40. 10.8 ALL 10.9 ALL

41. Essential Question: How do you use area of a circle to figure out radius of a circle?

42. πr 2 A= πr 2 r=6cm A= π(6) 2 A= 36π cm 2

43. A= πr 2 20π = πr 2 √ 20 = r 2√5≈4.47in = r

44. 5cm A= πr 2 A= π(5) 2 A= 25π cm 2

45. Essential Question: How do you use the area of only part of a circle?

46. Portion of a circle enclosed by 2 radii and an arc

47. Portion of a circle bounded by a chord and an arc

48. 60 8 2

49. 8π 12 2 8 x 360= (x) x 144 x 2880 = (x) x 144 20 = x

50. 120 24 2 =192π 24 60 30 12 12√3 192π – 249.42 = 353.77 u 2

51. 10.10 (#1 – 5, 11 – 13) 10.11 (#3 – 17)