Name: ________________________ Class: ___________________ Date: __________
ID: A
Circles Review
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. m∠O = 111
a.
____
291
b.
69
c.
55.5
d.
222
d.
19.3
2. BC 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.
a.
18.7
b.
18.1
c.
1
21.6
Name: ________________________
____
3. A chain fits tightly around two gears as shown. The distance between the centers of the gears is 20 inches.
The radius of the larger gear is 11 inches. Find the radius of the smaller gear. Round your answer to the
nearest tenth, if necessary. The diagram is not to scale.
a.
____
ID: A
17.2 inches
b.
6.2 inches
c.
11 inches
d.
4.8 inches
4. JK , KL, and LJ are all tangent to O (not drawn to scale). JA = 9, AL = 10, and
CK = 14. Find the perimeter of ∆JKL.
a.
66
b.
38
c.
2
46
d.
33
Name: ________________________

→
ID: A

→


→
In the figure, PA and PB are tangent to circle O and PD bisects ∠BPA. The figure is not drawn to
scale.
____
5. For m∠AOC = 46, find m∠POB.
a. 23
b. 90
c.
46
d.
68
Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to
scale.
____
6. NA ≅ PA , MO ⊥ NA, RO ⊥ PA , MN = 6 feet
a.
12 ft
b.
36 ft
c.
3
6 ft
d.
3 ft
Name: ________________________
____
____
____
ID: A
7.
a.
13
b.
26
c.
77
d.
38.5
a.
21.9
b.
181.3
c.
24
d.
13.5
a.
18.8
b.
120
c.
5.3
d.
12
8.
9.
4
Name: ________________________
ID: A
____ 10. The figure consists of a chord, a secant and a tangent to the circle. Round to the nearest hundredth, if
necessary.
a.
15.75
b.
9
c.
5.14
d.
28
c.
19.5
d.
15
____ 11. AB = 20, BC = 6, and CD = 8
a.
18.5
b.
11.5
5
Name: ________________________
ID: A
____ 12.
a.
19.34
b.
10.49
c.
110
d.
9.22
19
d.
20.5
____ 13. FG ⊥ OP , RS ⊥ OQ , FG = 40, RS = 37, OP = 19
a.
27.2
b.
18.5
c.
____ 14. WZ and XR are diameters. Find the measure of arc ZWX. (The figure is not drawn to scale.)
a.
226
b.
275
c.
6
39
d.
321
Name: ________________________
ID: A
____ 15. The circles are congruent. What can you conclude from the diagram?
a.
b.
arc CAB ≅ arc FDE
arc DF ≅ arc AC
c.
d.
arc AB ≅ arc DE
none of these
____ 16. m∠R = 22. Find m∠O. (The figure is not drawn to scale.)
a.
68
b.
22
c.
158
d.
44
____ 17. 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.)
a.
164
b.
303
c.
7
246
d.
262
Name: ________________________
ID: A
____ 18. Find the measure of ∠BAC. (The figure is not drawn to scale.)
a.
57
b.
28.5
c.
33
d.
114
c.
23
d.
46
____ 19. Find x. (The figure is not drawn to scale.)
a.
92
b.
44
8
Name: ________________________
ID: A
←
→
____ 20. BD is tangent to circle O at C, m(arc AEC) = 279, and m∠ACE = 85. Find m∠DCE.
(The figure is not drawn to scale.)
a.
109
b.
97
c.
54.5
d.
48.5
d.
80
____ 21. If m(arc BY) = 40, what is m∠YAC? (The figure is not drawn to scale.)
a.
140
b.
100
c.
9
70
Name: ________________________
ID: A
____ 22. m(arc DE) = 96 and m(arc BC) = 67. Find m∠A. (The figure is not drawn to scale.)
a.
14.5
b.
62.5
c.
81.5
d.
29
____ 23. m∠S = 36, m(arc RS) = 118, and RU is tangent to the circle at R. Find m∠U.
(The figure is not drawn to scale.)
a.
23
b.
82
c.
46
d.
41
____ 24. Find the diameter of the circle for BC = 16 and DC = 28. Round to the nearest tenth.
(The diagram is not drawn to scale.)
a.
33
b.
49
c.
10
14.3
d.
65
Name: ________________________
ID: A
____ 25. Compare the quantity in Column A with the quantity in Column B.
Column A
AP
a.
b.
c.
d.
Column B
AX
The quantity in Column A is greater.
The quantity in Column B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Write the standard equation for the circle.
____ 26. center (2, 7), r = 4
a.
(x – 7) 2 + (y – 2) 2 = 16
c.
(x – 2) 2 + (y – 7) 2 = 16
b.
(x – 2) 2 + (y – 7) 2 = 4
d.
(x + 2) 2 + (y + 7) 2 = 4
____ 27. center (–6, –8), that passes through (0, 0)
a.
(x – 6) 2 + (y – 8) 2 = 10
c.
(x + 6) 2 + (y + 8) 2 = 14
b.
(x – 6) 2 + (y – 8) 2 = 196
d.
(x + 6) 2 + (y + 8) 2 = 100
____ 28. Find the center and radius of the circle with equation ( x + 9) 2 + (y + 5) 2 = 64.
a. center (5, 9); r = 8
c. center (–9, –5); r = 64
b. center (9, 5); r = 64
d. center (–9, –5); r = 8
11
Name: ________________________
ID: A
____ 29. 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?
a.
(x – 6) 2 + (y – 1) 2 = 32
c.
(x – 6) 2 + (y – 1) 2 = 16
b.
(x + 6) 2 + (y + 1) 2 = 32
d.
(x + 6) 2 + (y + 1) 2 = 16
____ 30. Write the standard equation of the circle in the graph.
a.
(x + 3) 2 + (y – 2) 2 = 9
c.
(x – 3) 2 + (y + 2) 2 = 18
b.
(x – 3) 2 + (y + 2) 2 = 9
d.
(x + 3) 2 + (y – 2) 2 = 18
12
Name: ________________________
ID: A
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.)
32.
m∠A = 20 and m(arc BC) = 88 (The figure is not drawn to scale.)
a.
b.
Find x.
Find y.
13
ID: A
Circles Review
Answer Section
MULTIPLE CHOICE
1. ANS: B
PTS: 1
DIF: L2
REF: 12-1 Tangent Lines
OBJ: 12-1.1 Using the Radius-Tangent Relationship
NAT: NAEP 2005 G3e | ADP K.4
STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 D.1 | NJ 4.2.12 E.1c
TOP: 12-1 Example 1
KEY: tangent to a circle | point of tangency | properties of tangents | central angle
2. ANS: B
PTS: 1
DIF: L2
REF: 12-1 Tangent Lines
OBJ: 12-1.1 Using the Radius-Tangent Relationship
NAT: NAEP 2005 G3e | ADP K.4
STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 D.1 | NJ 4.2.12 E.1c
TOP: 12-1 Example 2
KEY: tangent to a circle | point of tangency | properties of tangents | Pythagorean Theorem
3. ANS: D
PTS: 1
DIF: L2
REF: 12-1 Tangent Lines
OBJ: 12-1.1 Using the Radius-Tangent Relationship
NAT: NAEP 2005 G3e | ADP K.4
STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 D.1 | NJ 4.2.12 E.1c
TOP: 12-1 Example 2
KEY: word problem | tangent to a circle | point of tangency | properties of tangents | right triangle |
Pythagorean Theorem
4. ANS: A
PTS: 1
DIF: L2
REF: 12-1 Tangent Lines
OBJ: 12-1.2 Using Multiple Tangents
NAT: NAEP 2005 G3e | ADP K.4
STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 D.1 | NJ 4.2.12 E.1c
TOP: 12-1 Example 5
KEY: properties of tangents | tangent to a circle | triangle
5. ANS: C
PTS: 1
DIF: L2
REF: 12-1 Tangent Lines
OBJ: 12-1.2 Using Multiple Tangents
NAT: NAEP 2005 G3e | ADP K.4
STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 D.1 | NJ 4.2.12 E.1c
TOP: 12-1 Example 4
KEY: properties of tangents | tangent to a circle | Tangent Theorem
6. ANS: D
PTS: 1
DIF: L2
REF: 12-2 Chords and Arcs
OBJ: 12-2.1 Using Congruent Chords, Arcs, and Central Angles
NAT: NAEP 2005 G3e | ADP K.4
STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1 | NJ 4.2.12 E.1b
TOP: 12-2 Example 2
KEY: circle | radius | chord | congruent chords | bisected chords
7. ANS: C
PTS: 1
DIF: L2
REF: 12-2 Chords and Arcs
OBJ: 12-2.1 Using Congruent Chords, Arcs, and Central Angles
NAT: NAEP 2005 G3e | ADP K.4
STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1 | NJ 4.2.12 E.1b
TOP: 12-2 Example 1
KEY: arc | central angle | congruent arcs
8. ANS: D
PTS: 1
DIF: L2
REF: 12-2 Chords and Arcs
OBJ: 12-2.2 Lines Through the Center of a Circle
NAT: NAEP 2005 G3e | ADP K.4
STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1 | NJ 4.2.12 E.1b
TOP: 12-2 Example 3
KEY: bisected chords | circle | perpendicular | perpendicular bisector | Pythagorean Theorem
1
ID: A
9. ANS:
REF:
NAT:
STA:
TOP:
10. ANS:
REF:
NAT:
STA:
KEY:
11. ANS:
REF:
NAT:
STA:
TOP:
12. ANS:
REF:
NAT:
STA:
TOP:
13. ANS:
OBJ:
NAT:
STA:
TOP:
KEY:
14. ANS:
OBJ:
NAT:
STA:
TOP:
KEY:
15. ANS:
OBJ:
NAT:
STA:
TOP:
16. ANS:
OBJ:
STA:
KEY:
17. ANS:
OBJ:
STA:
KEY:
D
PTS: 1
DIF: L2
12-4 Angle Measures and Segment Lengths
OBJ: 12-4.2 Finding Segment Lengths
NAEP 2005 G3e | ADP J.5.1 | ADP K.4
NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1
12-4 Example 3
KEY: circle | chord | intersection inside the circle
A
PTS: 1
DIF: L3
12-4 Angle Measures and Segment Lengths
OBJ: 12-4.2 Finding Segment Lengths
NAEP 2005 G3e | ADP J.5.1 | ADP K.4
NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1
circle | chord | intersection inside the circle | intersection outside the circle | secant | tangent to a circle
B
PTS: 1
DIF: L2
12-4 Angle Measures and Segment Lengths
OBJ: 12-4.2 Finding Segment Lengths
NAEP 2005 G3e | ADP J.5.1 | ADP K.4
NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1
12-4 Example 3
KEY: circle | intersection outside the circle | secant
B
PTS: 1
DIF: L2
12-4 Angle Measures and Segment Lengths
OBJ: 12-4.2 Finding Segment Lengths
NAEP 2005 G3e | ADP J.5.1 | ADP K.4
NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1
12-4 Example 3
KEY: segment length | tangent | secant
D
PTS: 1
DIF: L3
REF: 12-2 Chords and Arcs
12-2.1 Using Congruent Chords, Arcs, and Central Angles
NAEP 2005 G3e | ADP K.4
NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1 | NJ 4.2.12 E.1b
12-2 Example 3
circle | radius | chord | congruent chords | right triangle | Pythagorean Theorem
A
PTS: 1
DIF: L2
REF: 12-2 Chords and Arcs
12-2.1 Using Congruent Chords, Arcs, and Central Angles
NAEP 2005 G3e | ADP K.4
NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1 | NJ 4.2.12 E.1b
12-2 Example 1
arc | central angle | congruent arcs | arc measure | arc addition | diameter
C
PTS: 1
DIF: L2
REF: 12-2 Chords and Arcs
12-2.1 Using Congruent Chords, Arcs, and Central Angles
NAEP 2005 G3e | ADP K.4
NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1 | NJ 4.2.12 E.1b
12-2 Example 1
KEY: arc | central angle | congruent circles
D
PTS: 1
DIF: L2
REF: 12-3 Inscribed Angles
12-3.1 Finding the Measure of an Inscribed Angle
NAT: NAEP 2005 G3e | ADP K.4
NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a
TOP: 12-3 Example 2
circle | inscribed angle | intercepted arc | inscribed angle-arc relationship
D
PTS: 1
DIF: L2
REF: 12-3 Inscribed Angles
12-3.1 Finding the Measure of an Inscribed Angle
NAT: NAEP 2005 G3e | ADP K.4
NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a
TOP: 12-3 Example 2
circle | inscribed angle | intercepted arc | inscribed angle-arc relationship
2
ID: A
18. ANS:
OBJ:
STA:
KEY:
19. ANS:
OBJ:
STA:
KEY:
20. ANS:
OBJ:
STA:
KEY:
21. ANS:
OBJ:
STA:
KEY:
22. ANS:
REF:
NAT:
STA:
TOP:
KEY:
23. ANS:
REF:
NAT:
STA:
TOP:
KEY:
24. ANS:
REF:
NAT:
STA:
TOP:
KEY:
25. ANS:
REF:
NAT:
STA:
TOP:
KEY:
length
26. ANS:
REF:
OBJ:
STA:
TOP:
B
PTS: 1
DIF: L3
REF: 12-3 Inscribed Angles
12-3.1 Finding the Measure of an Inscribed Angle
NAT: NAEP 2005 G3e | ADP K.4
NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a
TOP: 12-3 Example 2
circle | inscribed angle | intercepted arc | inscribed angle-arc relationship
C
PTS: 1
DIF: L2
REF: 12-3 Inscribed Angles
12-3.1 Finding the Measure of an Inscribed Angle
NAT: NAEP 2005 G3e | ADP K.4
NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a
TOP: 12-3 Example 1
circle | inscribed angle | intercepted arc | inscribed angle-arc relationship
C
PTS: 1
DIF: L2
REF: 12-3 Inscribed Angles
12-3.2 The Angle Formed by a Tangent and a Chord
NAT: NAEP 2005 G3e | ADP K.4
NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a
TOP: 12-3 Example 3
circle | inscribed angle | tangent-chord angle | intercepted arc
C
PTS: 1
DIF: L2
REF: 12-3 Inscribed Angles
12-3.2 The Angle Formed by a Tangent and a Chord
NAT: NAEP 2005 G3e | ADP K.4
NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a
TOP: 12-3 Example 3
circle | inscribed angle | tangent-chord angle | intercepted arc | arc measure | angle measure
A
PTS: 1
DIF: L2
12-4 Angle Measures and Segment Lengths
OBJ: 12-4.1 Finding Angle Measures
NAEP 2005 G3e | ADP J.5.1 | ADP K.4
NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1
12-4 Example 1
circle | secant | angle measure | arc measure | intersection outside the circle
A
PTS: 1
DIF: L3
12-4 Angle Measures and Segment Lengths
OBJ: 12-4.1 Finding Angle Measures
NAEP 2005 G3e | ADP J.5.1 | ADP K.4
NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1
12-4 Example 1
circle | chord | angle measure | arc measure | intersection on the circle | intersection outside the circle
A
PTS: 1
DIF: L2
12-4 Angle Measures and Segment Lengths
OBJ: 12-4.2 Finding Segment Lengths
NAEP 2005 G3e | ADP J.5.1 | ADP K.4
NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1
12-4 Example 3
circle | intersection outside the circle | secant | tangent | diameter
B
PTS: 1
DIF: L3
12-4 Angle Measures and Segment Lengths
OBJ: 12-4.2 Finding Segment Lengths
NAEP 2005 G3e | ADP J.5.1 | ADP K.4
NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1
12-4 Example 3
circle | intersection outside the circle | secant | tangent | chord | intersection inside the circle | segment
C
PTS: 1
DIF: L2
12-5 Circles in the Coordinate Plane
12-5.1 Writing an Equation of a Circle
NAT: NAEP 2005 G4d | ADP K.10.4
NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 C.1a | NJ 4.3.12 B.1 | NJ 4.3.12 D.3
12-5 Example 1
KEY: equation of a circle | center | radius
3
ID: A
27. ANS:
REF:
OBJ:
STA:
TOP:
28. ANS:
REF:
OBJ:
STA:
TOP:
29. ANS:
REF:
OBJ:
STA:
TOP:
KEY:
30. ANS:
REF:
OBJ:
STA:
TOP:
KEY:
D
PTS: 1
DIF: L2
12-5 Circles in the Coordinate Plane
12-5.1 Writing an Equation of a Circle
NAT: NAEP 2005 G4d | ADP K.10.4
NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 C.1a | NJ 4.3.12 B.1 | NJ 4.3.12 D.3
12-5 Example 2
KEY: equation of a circle | center | radius | point on the circle
D
PTS: 1
DIF: L2
12-5 Circles in the Coordinate Plane
12-5.2 Finding the Center and Radius of a Circle
NAT: NAEP 2005 G4d | ADP K.10.4
NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 C.1a | NJ 4.3.12 B.1 | NJ 4.3.12 D.3
12-5 Example 3
KEY: center | circle | coordinate plane | radius
D
PTS: 1
DIF: L2
12-5 Circles in the Coordinate Plane
12-5.2 Finding the Center and Radius of a Circle
NAT: NAEP 2005 G4d | ADP K.10.4
NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 C.1a | NJ 4.3.12 B.1 | NJ 4.3.12 D.3
12-4 Example 4
center | circle | coordinate plane | radius | equation of a circle | word problem
B
PTS: 1
DIF: L2
12-5 Circles in the Coordinate Plane
12-5.2 Finding the Center and Radius of a Circle
NAT: NAEP 2005 G4d | ADP K.10.4
NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 C.1a | NJ 4.3.12 B.1 | NJ 4.3.12 D.3
12-4 Example 4
center | circle | coordinate plane | radius | equation of a circle
SHORT ANSWER
31. ANS:
No, because 7 2 + 3.75 2 ≠ 8 2 .
PTS: 1
DIF: L2
REF: 12-1 Tangent Lines
OBJ: 12-1.1 Using the Radius-Tangent Relationship
NAT: NAEP 2005 G3e | ADP K.4
STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 D.1 | NJ 4.2.12 E.1c
TOP: 12-1 Example 3
KEY: tangent to a circle | right triangle | Pythagorean Theorem | properties of tangents
32. ANS:
a. 48
b. 112
PTS: 1
DIF: L2
REF: 12-4 Angle Measures and Segment Lengths
OBJ: 12-4.1 Finding Angle Measures
NAT: NAEP 2005 G3e | ADP J.5.1 | ADP K.4
STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a | NJ 4.2.12 D.1
TOP: 12-4 Example 1
KEY: angle measure | angle-arc relationship | arc | arc addition | arc measure | circle | intercepted arc |
intersection outside the circle | intersection on the circle | secant | tangent to a circle | multi-part question
4