Tangent Lines Pages 586-589 Exercises 14. circumscribed about GEOMETRY LESSON 11-1 Pages 586-589 Exercises 14. circumscribed about 15. circumscribed about 16. 78 cm 17. 14.2 in. 18. 68 cm 19. 27.6 m 20. 13 21. 3.6 cm 1. 120 2. 47 3. 30 4. 14.04 in. 5. Extend RS and QP until they meet at a point, H. By Thm. 11-3, RH = QH, or SH + RS = QP + PH. By 11-3 again, SH = PH. Thus, RS = QP. 6. 15.2 cm 7. 20.0 in. 8. 14.0 in. 9. 19.1 cm 10. No; 52 + 162 162 11. Yes; 2.52 + 62 = 6.52 12. Yes; 62 + 82 = 102 13. inscribed in = / 11-1

d. blue lines; green lines e. No; explanations may vary. Tangent Lines GEOMETRY LESSON 11-1 29. about 34.6 in. 30. a. b. 3 c. Kites; two pairs of adj. sides are but no opp. sides are . (Special case: for a rt. isosc. , one kite is a square.) 22. 8 in. 23. a. external b. external c. internal d. blue lines; green lines e. No; explanations may vary. 24. 35.8 km 25. 80.0 km 26. 113.1 km 27. 57.5 28. a. b. Answers may vary. Sample: If you draw diagonals in the small square, 8 are formed in the entire figure with 4 in the small square. s 11-1

d. AB || CD; arguments may vary. Tangent Lines GEOMETRY LESSON 11-1 37. a–c.      d. AB || CD; arguments may vary. 31. All four are ; the two tangents to each coin from A are , so by the Trans. Prop., all are . 32. 33. 35 34. 90 – or ; m 4 is m 1. 35. 4 units 36. about 5.2 in. 180 – x 2 x 1 11-1

40. 1. BA and BC are tangent to O at A and C (Given) Tangent Lines GEOMETRY LESSON 11-1 38. Assume AB is not tangent to O. Then either AB does not intersect O or AB intersects O at two pts. If AB does not intersect O, then P is not on O, which contradicts OP being a radius. If AB intersects O at two pts., P and Q, then OP OQ ( radii), OPQ is isosc., and OPQ OQP. But OPQ is a rt. , since AB OP, and OPQ has two rt. . This is a contradiction also, so AB is tangent to O. 39. 88.2 cm2 40. 1.  BA and BC are tangent to O at A and C (Given)  2.  AB OA and BC OC (If a line is tan. to a circle, it is to the radius.)  3.  BAO and BCO are right . (Def. of rt. )  40. (continued) 4.  AO OC (Radii of a circle are .)  5.  BO BO (Refl. Prop. of )  6.  BAO BCO (HL Thm.)  7.  BA BC (CPCTC) . s 11-1

42. 1. A and B with common tangents DF and CE (Given) Tangent Lines GEOMETRY LESSON 11-1 42. 1.  A and B with common tangents DF and CE (Given)  2. GD = GC and GE = GF (Two tan. segments from a pt. to a circle are .)  3.  = 1, = 1 (Div. Prop. of =) 4.  (Trans. Prop. of =)  42. (continued) 5. DGC EGF (Vert. are .)  6. GDC ~ GFE (SAS ~ Thm.) 43. C 44. F 45. C 46. I 41. 1. BC is tangent to A at D. (Given)  2. DB DC (Given)  3. AD BC (If a line is tan. to a circle, it is to the radius.)  4.  ADB and ADC are rt. (Def. of rt. )  5. AD AD (Refl. Prop. of )  6.  ADB ADC (SAS)  7.  AB AC (CPCTC) . s GD GC GF GE = 11-1

OR equivalent solution Tangent Lines GEOMETRY LESSON 11-1 52. 28.1 53. 68.2 54. a. 10:17 b. m = 1.82; n = 3.78 55. a. 4:1 b. a = 1.625; b = 1.75, c = 3 47. [2]   = 2x = 9  x = 4.5 OR equivalent solution [1] correct eq. solved incorrectly 48. 3:4 49. 9:16 50. 27:64 51. 29.1 2 3 x 11-1