ExamView - circles test review - Mendham Borough · PDF fileWrite the standard equation for the circle. ... r = 4 a. (x – 7)2 + (y – 2)2 = 16 c. (x – 2)2 + (y – 7)2 = 16 b

Name: ________________________ Class: ___________________ Date: __________ ID: A

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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

____ 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. 21.6 d. 19.3

Name: ________________________ ID: A

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____ 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. 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. 46 d. 33

Name: ________________________ ID: A

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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. 6 ft d. 3 ft

Name: ________________________ ID: A

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____ 7.

a. 13 b. 26 c. 77 d. 38.5

____ 8.

a. 21.9 b. 181.3 c. 24 d. 13.5

____ 9.

a. 18.8 b. 120 c. 5.3 d. 12

Name: ________________________ ID: A

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____ 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

____ 11. AB = 20, BC = 6, and CD = 8

a. 18.5 b. 11.5 c. 19.5 d. 15

Name: ________________________ ID: A

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____ 12.

a. 19.34 b. 10.49 c. 110 d. 9.22

____ 13. FG ⊥ OP, RS ⊥ OQ , FG = 40, RS = 37, OP = 19

a. 27.2 b. 18.5 c. 19 d. 20.5

____ 14. WZ and XR are diameters. Find the measure of arc ZWX. (The figure is not drawn to scale.)

a. 226 b. 275 c. 39 d. 321

Name: ________________________ ID: A

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____ 15. The circles are congruent. What can you conclude from the diagram?

a. arc CAB ≅ arc FDE c. arc AB ≅ arc DE

b. arc DF ≅ arc AC d. 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. 246 d. 262

Name: ________________________ ID: A

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____ 18. Find the measure of ∠BAC. (The figure is not drawn to scale.)

a. 57 b. 28.5 c. 33 d. 114

____ 19. Find x. (The figure is not drawn to scale.)

a. 92 b. 44 c. 23 d. 46

Name: ________________________ ID: A

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____ 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

____ 21. If m(arc BY) = 40, what is m∠YAC? (The figure is not drawn to scale.)

a. 140 b. 100 c. 70 d. 80

Name: ________________________ ID: A

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____ 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. 14.3 d. 65

Name: ________________________ ID: A

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____ 25. Compare the quantity in Column A with the quantity in Column B.

Column A Column B

AP AX

a. The quantity in Column A is greater.

b. The quantity in Column B is greater.

c. The two quantities are equal.

d. 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

Name: ________________________ ID: A

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____ 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

Name: ________________________ ID: A

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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. Find x.

b. Find y.

ID: A

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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



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



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


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


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




TOP: 12-2 Example 1 KEY: arc | central angle | congruent arcs


OBJ: 12-2.2 Lines Through the Center of a Circle NAT: NAEP 2005 G3e | ADP K.4


TOP: 12-2 Example 3

KEY: bisected chords | circle | perpendicular | perpendicular bisector | Pythagorean Theorem

ID: A

2

9. ANS: D PTS: 1 DIF: L2

REF: 12-4 Angle Measures and Segment Lengths OBJ: 12-4.2 Finding Segment Lengths

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 3 KEY: circle | chord | intersection inside the circle

10. ANS: A PTS: 1 DIF: L3




KEY: circle | chord | intersection inside the circle | intersection outside the circle | secant | tangent to a circle

11. ANS: B PTS: 1 DIF: L2




TOP: 12-4 Example 3 KEY: circle | intersection outside the circle | secant





TOP: 12-4 Example 3 KEY: segment length | tangent | secant





TOP: 12-2 Example 3

KEY: circle | radius | chord | congruent chords | right triangle | Pythagorean Theorem

14. ANS: A PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs




TOP: 12-2 Example 1

KEY: arc | central angle | congruent arcs | arc measure | arc addition | diameter

15. ANS: C PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs




TOP: 12-2 Example 1 KEY: arc | central angle | congruent circles

16. ANS: D PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles

OBJ: 12-3.1 Finding the Measure of an Inscribed Angle NAT: NAEP 2005 G3e | ADP K.4

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4a TOP: 12-3 Example 2

KEY: circle | inscribed angle | intercepted arc | inscribed angle-arc relationship

17. ANS: D PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles




ID: A

3

18. ANS: B PTS: 1 DIF: L3 REF: 12-3 Inscribed Angles




19. ANS: C PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles





OBJ: 12-3.2 The Angle Formed by a Tangent and a Chord NAT: NAEP 2005 G3e | ADP K.4


KEY: circle | inscribed angle | tangent-chord angle | intercepted arc


OBJ: 12-3.2 The Angle Formed by a Tangent and a Chord NAT: NAEP 2005 G3e | ADP K.4


KEY: circle | inscribed angle | tangent-chord angle | intercepted arc | arc measure | angle measure


REF: 12-4 Angle Measures and Segment Lengths OBJ: 12-4.1 Finding Angle Measures



TOP: 12-4 Example 1

KEY: circle | secant | angle measure | arc measure | intersection outside the circle


REF: 12-4 Angle Measures and Segment Lengths OBJ: 12-4.1 Finding Angle Measures



TOP: 12-4 Example 1

KEY: circle | chord | angle measure | arc measure | intersection on the circle | intersection outside the circle





TOP: 12-4 Example 3

KEY: circle | intersection outside the circle | secant | tangent | diameter





TOP: 12-4 Example 3

KEY: circle | intersection outside the circle | secant | tangent | chord | intersection inside the circle | segment

length

26. ANS: C PTS: 1 DIF: L2

REF: 12-5 Circles in the Coordinate Plane

OBJ: 12-5.1 Writing an Equation of a Circle NAT: NAEP 2005 G4d | ADP K.10.4

STA: 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

TOP: 12-5 Example 1 KEY: equation of a circle | center | radius

ID: A

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OBJ: 12-5.1 Writing an Equation of a Circle NAT: NAEP 2005 G4d | ADP K.10.4


TOP: 12-5 Example 2 KEY: equation of a circle | center | radius | point on the circle



OBJ: 12-5.2 Finding the Center and Radius of a Circle NAT: NAEP 2005 G4d | ADP K.10.4


TOP: 12-5 Example 3 KEY: center | circle | coordinate plane | radius





TOP: 12-4 Example 4

KEY: center | circle | coordinate plane | radius | equation of a circle | word problem





TOP: 12-4 Example 4

KEY: center | circle | coordinate plane | radius | equation of a circle

SHORT ANSWER

31. ANS:

No, because 72+ 3.75

2≠ 8

2.

PTS: 1 DIF: L2 REF: 12-1 Tangent Lines



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


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

Documents

ExamView - circles test review - Mendham Borough · PDF fileWrite the standard equation for the circle. ... r = 4 a. (x – 7)2 + (y – 2)2 = 16 c. (x – 2)2 + (y – 7)2 = 16 b