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Warm-Up

Warm-Up. 19. TCH 21. 52 23. There are none shown in the pict. 25. 23.5 26. 3 27. 102 28. 60 29. 60 30. 60 37. 89 38. 91 39. 114 40. 90 41. 33 42. 33 43. 44.5 44. 57 45. 78.5. p. 462 #17-22, 25, 27, 32-34 17. S 18. 18 19. PQ, UV, UW 20. DU, DV, DT, DR

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Warm-Up

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  1. Warm-Up 19. TCH 21. 52 23. There are none shown in the pict. 25. 23.5 26. 3 27. 102 28. 60 29. 60 30. 60 37. 89 38. 91 39. 114 40. 90 41. 33 42. 33 43. 44.5 44. 57 45. 78.5 p. 462 #17-22, 25, 27, 32-34 17. S 18. 18 19. PQ, UV, UW 20. DU, DV, DT, DR 21. Neither, they are congruent 22. 21.3 25. 28 27. 21 32. 8.7 33. 24 34. 4 p. 470 #7-23 odd, 25-30, 37-45 7. BC 9. 40 11. 72 13. 104 15. 52 17. HC

  2. Today’s Agenda • Warm-Up • Quiz 9.1-9.4 • 9-5: Tangents • What is a tangent line and what relationships occur with them? • Practice • Assign Homework

  3. Quiz • Quiz 9.1-9.4. • Good Luck!! • You have 30 minutes!!!

  4. 9-5 Tangents • Tangent: a line that intersects the circle in exactly one point. • Point of Tangency: The point where a tangent and the circle intersect. Point of Tangency

  5. Theorem • Theorem 9-8:If a line is tangent to a circle then it is perpendicular to the radius drawn to the point of tangency.

  6. x 6 in A C B 8 in Example • Find x. (AB is a tangent line.)

  7. A D C B Theorem • Theorem 9-9: In a plane, if a line is perpendicular to a radius of a circle at the endpoint on the circle, then the line is a tangent to the circle. If AB I CD, then CD is a tangent line.

  8. A 17 in 7 in C D B 24 in Example • Is Line BC a tangent line?

  9. Common Tangent • Common Tangent: a line or line segment that is tangent to two circles in the same plane.

  10. Common External Tangents • Common External Tangents: a common tangent that does not intersect the segment whose endpoints are the center of the circles.

  11. Common Internal Tangents • Common Internal Tangents: a common tangent that does intersect the segment whose endpoints are the centers of the circles.

  12. Tangent Segments • Tangent Segments: a segment AB such that one endpoint is on a circle, the other is outside the circle and the line AB is tangent to the circle.

  13. Theorem • Theorem 9-10: If 2 segments from the same exterior point are tangent to a circle, then they are congruent.

  14. Example • Find x, the diameter of the circle is 6 ft. 49° x

  15. Circumscribed Polygons • Circumscribed Polygons: a polygon is circumscribed about a circle if each side of the polygon is tangent to the circle.

  16. Homework • p. 479 #17-25, 29, 31-36 • Chapter 9 Test ( )

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