Chapter 9 Circles

1. Chapter 9Circles • Define a circle and a sphere. • Apply the theorems that relate tangents, chords and radii. • Define and apply the properties of central angles and arcs.

2. Bring a Compass Tomorrow

3. 9.1 Basic Terms Objectives • Define and apply the terms that describe a circle.

4. is a set of points in a plane equidistant from a given point. The Circle B A

5. The given distance is a radius (plural radii) The Circle B radius A

6. The given point is the center The Circle B radius A center

7. The Circle B Point on circle A

8. Chord any segment whose endpoints are on the circle. C B chord A

9. Diameter A chord that contains the center of the circle C B A diameter

10. Secant any line that contains a chord of a circle. C B secant A

11. any line that contains exactly one point on the circle. Tangent B A tangent

12. Point of Tangency B Point of tangency A

13. is the set of all points equidistant from a given point. Sphere B A

14. Radii Diameter Chord Secant Tangent Sphere C E B A F D

15. have equal radii. Congruent Circles (or Spheres) B E D A

16. Concentric Circles (or Spheres) share the same center. G O Q

17. Inscribed/Circumscribed A polygon is inscribed in a circle and the circle is circumscribed about the polygon if each vertex of the polygon lies on the circle.

18. L N M O Q R Name each segment P

19. L N M O Q R OM P

20. L N M O Q R MN P

21. L N M O Q R MN P

22. L N M O Q R MQ P

23. L N M O Q R ML P

24. L N M O Q R ML P

25. L N M O Q R Point M P

26. 9.2 Tangents Objectives • Apply the theorems that relate tangents and radii

27. Theorem If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. B A tangent C Sketch

28. Corollary Tangents to a circle from a common point are congruent. Y tangent A X tangent Z Sketch

29. Theorem If a line in the plane of a circle is perpendicular to a radius at its endpoint, then the line is a tangent to the circle. B tangent A X

30. Inscribed/Circumscribed When each side of a polygon is tangent to a circle, the polygon is said to be circumscribed about the circle and the circle is inscribed in the polygon.

31. White Board Practice

32. Common Tangents are lines tangent to more than one coplanar circle. B tangent R A X

33. Common External Tangents X B R A

34. Common External Tangents R A X B

35. Common InternalTangents B R A X

36. Common InternalTangents X R A B

37. Construction 8 Given a point on a circle, construct the tangent to the circle through the point. Given: Construct: Steps:

38. Remote Time • How many common external tangents can be drawn?

39. Remote Time • How many common external tangents can be drawn?

40. Remote Time • How many common external tangents can be drawn?

41. Remote Time • How many common external tangents can be drawn?

42. Remote Time • How many common external tangents can be drawn?

43. Remote Time • How many common external tangents can be drawn?

44. Remote Time • How many common internal tangents can be drawn?

45. Remote Time • How many common internal tangents can be drawn?

46. Remote Time • How many common internal tangents can be drawn?

47. Remote Time • How many common internal tangents can be drawn?

48. Remote Time • How many common internal tangents can be drawn?

49. Remote Time • How many common internal tangents can be drawn?

50. Tangent Circles are circles that are tangent to each other. B R A