1. Chapter 10.6

2. Circle  A set of all points equidistant from the center

3. Circle  A circle is named by the center

4. Diameter  A segment that contains the center of a circle and has both endpoints on the circle.

5. Radius  A segment that has one endpoint at the center of the circle and the other on the circle.

6. Congruent Circles  Congruent circles have the congruent radii

7. Central Angle  An angle whose vertex is the center of the circle.

8. Arc  Part of a circle. From point to point on the outside of the circle.

9. Semicircle  An arc that’s half of the circle. Has a measure of 180 0

10. Minor Arc  A minor arc is smaller than half the circle. Same measure as the corresponding interior angle

11. Major Arc  A major arc is larger than half the circle. 360 minus the minor arc

12. Practice 1 Name 3 of the following in  A. 1. the minor arcs 2. the major arcs 3. the semicircles

13. Adjacent Arcs  Adjacent arcs are arcs of the same circle that have exactly one point in common.

14. Arc Addition Postulate  The measure of the arc formed by two adjacent arcs is the sum of the measure of the two arcs.

15. Practice 2  Find the measure of each arc in R. 1. UT 2. UV 3. VUT 4. ST 5. VS

16. Practice 3  Find each indicated measure for D. 1. m  EDI 2. 3. m  IDH 4.

17. Circumference  The distance around the circle  A measure of length

18. Circumference  The circumference of a circle is π times the diameter (a = πd) or 2 times π and the radius (a = 2πr).

19. Circumference  Example:

20. Circumference  Example:

21. Practice 4  Find the circumference of each circle. Leave your answer in terms of . 1. 2.

22. Arc Length  The length of an arc is calculated using the equation:

23. Arc Length  The length of an arc is calculated using the equation:

24. Arc Length  The length of an arc is calculated using the equation:

25. Arc Length

28. Practice 5  Find the length of each darkened arc. Leave your answer in terms of . 1. 2.

29. Area of a Circle  The product of π and the square of the radius.

30. Area of a Circle  Example:

31. Practice 6  Find the area of a circle: 1. 6 in. radius 2. 10 cm. radius 3. 12 ft. diameter

32. Sector of a Circle  A sector of a circle is a region bounded by an arc of the circle and the two radii to the arc’s endpoints.  You name a sector using the two endpoints with the center of the circle in the middle.

33. Sector of a Circle  Sector is the area of part of the circle

34. Area of Sector of a Circle  The area of a sector is:

35. Sector of a Circle  Find the area of the sector

36. Arc Length

39. Segment of a Circle  Part of a circle bounded by an arc and the segment joining its endpoints

40. Area of a Segment of a Circle  Equal to the area of the sector minus the area of a triangle who both use the center and the two endpoints of the segment.

41.  Sector – Triangle = Segment Area of a Segment of a Circle

42.  Find the area of the segment.

43. Area of a Segment of a Circle  Separate the triangle and the sector

44. Area of a Segment of a Circle  Find the area of both figures

45. Area of Sector

46. Area of Triangle

48. Area of a Segment of a Circle  Subtract the triangle from the Sector