Chapter 12 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.) 1. 111 Q P
x°
x°
a. 291 2. 3.
O
b. 69
c. 55.5
O
d. 222
a. 78
b. 39
c. 102
b. 7
c. 13
d. 24
12 is tangent to circle A at B and to circle D at C (not drawn to scale). AB = 7, BC = 18, and DC = 5. Find AD to the nearest tenth.
B C
A
D
a. 18.7 b. 18.1 c. 21.6 d. 19.3 4. is tangent to circle O at B. Find the length of the radius r for AB = 5 and AO = 8.6. Round to the nearest tenth if necessary. The diagram is not to scale.
A
B r O
a. 9.9 5.
d. 3.6
and are all tangent to O (not drawn to scale). JA = 9, AL = 10, and CK = 14. Find the perimeter of .
a. 66
b. 38
c. 46
d. 33
J
A
B O
L
K C
6.
Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale. 8. D
23
C
7
P x
x°
A a. 13
b. 26
a. 21.9
B c. 77
d. 38.5
b. 181.3
c. 24
d. 13.5
9.
10
7.
6
8
8 x
x
a. 18.8 a. 8
b. 5
c. 6
b. 120
c. 5.3
15
d. 12
d. 10
10. The figure consists of a chord, a secant and a tangent to the circle. Round to the nearest hundredth, if necessary.
4
9 7 x
a. 15.75
b. 9
c. 5.14
15
d. 28
11. AB = 20, BC = 6, and CD = 8
x D C B A
a. 18.5
b. 11.5
12.
c. 19.5
d. 15
x 5
17
a. 19.34
b. 10.49
c. 110
d. 9.22
13. The circles are congruent. What can you conclude from the diagram?
B
)
C
F
)
O
P
A
D E
a. arc CAB
arc FDE
Use the diagram.
b. arc DF
arc AC
c. arc AB
is a diameter, and
arc DE
d. none of these
. The figure is not drawn to scale.
C
A
P
B
D 14. Find a. 73.5
for b. 114 c. 132
= 66. d. 57
15. Which statement is NOT true? a. arc AC arc BD b. c. d.
C A
B
16. Find m(arc BD) for m(arc AC) = 43. a. 137° b. 133° c. 86° d. 47°
O
17. The radius of circle O is 18, and OC = 13. Find AB. Round to the nearest tenth, if necessary. (The figure is not drawn to scale.) a. 12.4
b. 3.8
c. 24.9
d. 44.4
18. m R = 22. Find m O. (The figure is not drawn to scale.)
d
N
O a
O
c
b
Q
a. 68
R c. 158
b. 22
a. a = 53° d. 44
19. Given that DAB and DCB are right angles and m BDC = 41, what is the measure of arc CAD? (The figure is not drawn to scale.)
b. b = 106°
c. c = 73°
21. If m(arc BY) = 40, what is m YAC? (The figure is not drawn to scale.) B Y
A
O D
B
a. 140
b. 100
A c. 70
C a. 164
b. 303
c. 246
d. d = 37°
d. 262
20. Find the measures of the indicated angles. Which statement is NOT true? (The figure is not drawn to scale.) 22. m(arc DE) = 96 and m(arc BC) = 67. Find m A. (The figure is not drawn to scale.)
C d. 80
D B A C E
a. 14.5 b. 62.5 c. 81.5 d. 29 23. Find the value of x for m(arc AB) = 46 and m(arc CD) = 25. (The figure is not drawn to scale.) D C
R
S
U
T
O x a. 23
b. 82
c. 46
d. 41
A 25. Find the diameter of the circle for BC = 16 and DC = 28. Round to the nearest tenth. (The diagram is not drawn to scale.) D C
B a. 35.5
b. 58.5
c. 71
d. 21
24. m S = 36, m(arc RS) = 118, and the circle at R. Find m U. (The figure is not drawn to scale.)
is tangent to
O
B
A
a. 33 Write the standard equation for the circle. 26. center (2, 7), r = 4 a. (x – 7) + (y – 2) = 16 b. (x – 2) + (y – 7) = 4 c. (x – 2) + (y – 7) = 16 d. (x + 2) + (y + 7) = 4 27. center (–6, –8), that passes through (0, 0)
b. 49
c. 14.3
d. 65
a. (x – 6) + (y – 8) = 10 b. (x – 6) + (y – 8) = 196 c. (x + 6) + (y + 8) = 14 d. (x + 6) + (y + 8) = 100
y
28. The center of a circle is (h, 7) and the radius is 10. The circle passes through (3, –1). Find all possible values of h. a. 8, –7 b. 9, –3 c. 9, –5 d. 10, 3
8
4
29. Find the center and radius of the circle with equation (x + 9) + (y + 5) = 64. a. center (5, 9); r = 8 b. center (9, 5); r = 64 c. center (–9, –5); r = 64 d. center (–9, –5); r = 8
–8
O
–4
4
8
x
–4
30. A low-wattage radio station can be heard only within a certain distance from the station. On the graph below, the circular region represents that part of the city where the station can be heard, and the center of the circle represents the location of the station. Which equation represents the boundary for the region where the station can be heard?
–8
a. (x – 6) + (y – 1) = 32 b. (x + 6) + (y + 1) = 32 c. (x – 6) + (y – 1) = 16 d. (x + 6) + (y + 1) = 16
Short Answer 31. Determine whether a tangent line is shown in the diagram, for AB = 7, OB = 3.75, and AO = 8. Explain your reasoning. (The figure is not drawn to scale.) B A
b. Is the triangle equilateral, isosceles, or scalene? Explain.
P (6x)°
(8x – 10)°
O
R 32. In , NL = NM, and the perimeter is 46 cm. A, B, and C are points of tangency to the circle. MC = 4 cm. Find NL. Explain your reasoning. (The figure is not drawn to scale.)
C
N
Q (10x + 10)° 34.
m A = 20 and m(arc BC) = 88 (The figure is not drawn to scale.)
M
B
A
x°
B
D
A
L C
33. a. Find x. (The figure is not drawn to scale.)
a. b.
Find x. Find y.
)
y°
35. The diameter of a circle has endpoints P(–10, –8) and Q(4, 4). a. Find the center of the circle. b. Find the radius. If your answer is not an integer, express it in radical form. c. Write an equation for the circle. 36. Graph the circle with equation (x + 1) + (y – 3) = 9. Other 37. Show that it is not possible for the lengths of the segments of two intersecting chords to be four consecutive integers.
m +2 m
m +3
m +1
Chapter 12 Practice Test Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS:
B A B B A C D D D A B B C D A A C D D C C A A A A C D B D D
TOP: TOP: TOP: TOP: TOP: TOP: TOP: TOP: TOP:
12-1 Example 1 12-1 Example 1 12-1 Example 2 12-1 Example 3 12-1 Example 5 12-2 Example 1 12-2 Example 3 12-2 Example 3 12-4 Example 3
TOP: 12-4 Example 3 TOP: 12-4 Example 3 TOP: 12-2 Example 1 TOP: TOP: TOP: TOP: TOP: TOP: TOP: TOP: TOP: TOP: TOP: TOP: TOP:
12-2 Example 3 12-2 Example 3 12-2 Example 3 12-3 Example 2 12-3 Example 2 12-3 Example 2 12-3 Example 3 12-4 Example 1 12-4 Example 1 12-4 Example 1 12-4 Example 3 12-5 Example 1 12-5 Example 2
TOP: 12-5 Example 3 TOP: 12-4 Example 4
SHORT ANSWER 31. ANS: No, because TOP: 12-1 Example 3 32. ANS:
.
and, by the Tangent Theorem, NC = NA. By subtraction, . Also by the Tangent Theorem, and , so . The perimeter is 46 cm, so . By substitution, , so . Since , , or 19 cm. TOP: 12-1 Example 5 33. ANS: a. 15 b. Scalene; the arc measures are 110°, 90°, and 160°. Since the arcs are not congruent, neither are the chords that intercept them. 34. ANS: a. 48 b. 112 TOP: 12-4 Example 1 35. ANS: a. (–3, –2) b. c. (x + 3) + (y + 2) = 85 36. ANS: y 8 4
–8
–4
O
4
8
x
–4 –8
TOP: 12-5 Example 3 OTHER 37. ANS: Let m, m + 1, m + 2, and m + 3 represent the four consecutive numbers. Then the product of the greatest and least numbers will equal the product of the two consecutive middle numbers. Solving the equation m(m + 3) = (m + 1)(m + 2) for m results in m2 + 3m = m2 + 3m + 2, or 0 = 2, which is false. TOP: 12-4 Example 3
