1. Tangent Lines Pages 586-589 Exercises 14. circumscribed about
GEOMETRY LESSON 11-1
Pages Exercises
14. circumscribed about
15. circumscribed about cm
in. cm m
20. 13 cm
1. 120
2. 47
3. 30
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. cm
in.
in. cm
10. No;
11. Yes; = 6.52
12. Yes; = 102
13. inscribed in = /
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2. 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.)
in.
23. a. external
b. external
c. internal
d. blue lines; green lines
e. No; explanations may vary. km km km
28. a.
b. Answers may vary. Sample: If you draw diagonals in the small square, are formed in the entire figure with 4 in the small square. s
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3. 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
– or ; m 4 is m 1.
35.
4 units
36. about 5.2 in.
180 – x 2 x 1
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4. 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.
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
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5. 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 =
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6. OR equivalent solution
Tangent Lines
GEOMETRY LESSON 11-1
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 2 3 x
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