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

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Geometry SIA #4, Review #2

Short Answer

1. Based on the pattern, what are the next two terms of the sequence?7, 15, 23, 31, . . .

2. Based on the pattern, what are the next two terms of the sequence?

7,74

,716

,764

,7

256, . . .

3. What conjecture can you make about the eleventh figure in this pattern?

4. What conjecture can you make about the twenty-fourth term in the pattern A, B, A, C, A, B, A, C?

5. What conjecture can you make about the sum of the first 19 odd numbers?

6. What conjecture can you make about the sum of the first 15 positive even numbers?2 = 2 = 1 22 + 4 = 6 = 2 32 + 4 + 6 = 12 = 3 42 + 4 + 6 + 8 = 20 = 4 52 + 4 + 6 + 8 + 10 = 30 = 5 6

7. Alfred is practicing typing. The first time he tested himself, he could type 39 words per minute. After practicing for a week, he could type 42 words per minute. After two weeks he could type 45 words per minute. Based on this pattern, predict how fast Alfred will be able to type after 4 weeks of practice.

8. What is a counterexample for the conjecture?Conjecture: Any number that is divisible by 5 is also divisible by 10.

9. What is the conclusion of the following conditional?A number is divisible by 3 if the sum of the digits of the number is divisible by 3.

10. Identify the hypothesis and conclusion of this conditional statement:If tomorrow is Thursday, then yesterday was Tuesday.

Name: ________________________ ID: A

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11. What is the converse of the following conditional?If a number is divisible by 6, then it is divisible by 2.

12. If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.Statement 1: If x = 7, then 9x – 4 = 59.Statement 2: x = 7

13. Use the Law of Detachment to draw a conclusion from the two given statements.

If two angles are congruent, then they have equal measures.

K and L are congruent.

14. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.I can go to the concert if I can afford to buy a ticket.I can go to the concert.

15. Use the Law of Syllogism to draw a conclusion from the two given statements.If it is Friday, then there is a math quiz.If there is a math quiz, then Jason is happy.

16. Use the Law of Syllogism to draw a conclusion from the two given statements.If two lines intersect and form right angles, then the lines are perpendicular.If two lines are perpendicular, then they intersect and form 90° angles.

17. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements.If it is Friday night, then there is a football game.If there is a football game, then Josef is wearing his school colors.It is Friday night.

18. What are the minor arcs of O?

Name: ________________________ ID: A

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19. What are the major arcs of O that contain point M?

20. Find the measure of CDE.The figure is not drawn to scale.

Find the circumference. Leave your answer in terms of .

21.

22.

Name: ________________________ ID: A

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23. The circumference of a circle is 38 cm. Find the diameter, the radius, and the length of an arc of 100°.

24. Find the length of YPX . Leave your answer in terms of .

Find the area of the circle. Leave your answer in terms of .

25.

26.

27. A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position. The team then measured the distance the wheel had rolled and found it to be 15 cm. To the nearest tenth, what is the area of the wheel?

28. Find the area of the figure to the nearest tenth.

29. Find the area of a sector with a central angle of 120° and a diameter of 9.9 cm. Round to the nearest tenth.

Name: ________________________ ID: A

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30. The area of sector AOB is 110.25 cm2 . Find the exact area of the shaded region.

31. Find the area of the shaded region. Leave your answer in terms of and in simplest radical form.

32. Find the exact area of the shaded region.

33. Find the probability that a point chosen at random from JT is on the segment KS .

34. Lenny’s favorite radio station has this hourly schedule: news 17 min, commercials 3 min, music 40 min. If Lenny chooses a time of day at random to turn on the radio to his favorite station, what is the probability that he will hear the news?

Name: ________________________ ID: A

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35. The delivery van arrives at an office every day between 3 PM and 5 PM. The office doors were locked between 3:10 PM and 3:30 PM. What is the probability that the doors were unlocked when the delivery van arrived?

36. Find the probability that a point chosen at random will lie in the shaded area.

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.)

37. mO 141

38. mP 12

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.

39. For mAOC = 41, find mPOB.

40. For mAOC = 54, find mBPO.

41. AB is tangent to O. If AO 8 and BC 9, what is AB?

The diagram is not to scale.

Name: ________________________ ID: A

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42. A satellite is 11,800 miles from the horizon of Earth. Earth’s radius is about 4,000 miles. Find the approximate distance the satellite is from the point directly below it on Earth’s surface.The diagram is not to scale.

43. BC is tangent to circle A at B and to circle D at C (not drawn to scale). AB = 7, BC = 16, and DC = 4. Find AD to the nearest tenth.

44. A chain fits tightly around two gears as shown. The distance between the centers of the gears is 23 inches. The radius of the larger gear is 9 inches. Find the radius of the smaller gear. Round your answer to the nearest tenth, if necessary. The diagram is not to scale.

Name: ________________________ ID: A

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45. AB is tangent to circle O at B. Find the length of the radius r for AB = 8 and AO = 11.5. Round to the nearest tenth if necessary. The diagram is not to scale.

46. Pentagon RSTUV is circumscribed about a circle. Solve for x for RS = 6, ST = 11, TU = 15, UV = 14, and VR = 12. The figure is not drawn to scale.

47. JK , KL, and LJ are all tangent to circle O (not drawn to scale), and JK LJ . JA = 8, AL = 12, and CK = 11. Find the perimeter of JKL.

Name: ________________________ ID: A

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48. In circle A, NA PA, MO NA, RO PA, MO = 10 ftWhat is PO?

49. In circle Z, BZ FZ, BZ CA, FZ DC, DF = 40 in.What is BC?

Name: ________________________ ID: A

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Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle. The figure is not drawn to scale.

50.

51.

52.

Name: ________________________ ID: A

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53. FG OP, RS OQ , FG = 29, RS = 31, OP = 15

Use the diagram. AB is a diameter, and AB CD. The figure is not drawn to scale.

54. Find m BD for m AC = 32.

Name: ________________________ ID: A

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

56. The radius of circle O is 23, and OC = 10. Find AB. Round to the nearest tenth, if necessary. (The figure is not drawn to scale.)

57. Find the measure of BAC in circle O. (The figure is not drawn to scale.)

Name: ________________________ ID: A

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58. Find x in circle O. (The figure is not drawn to scale.)

59. Find mBAC in circle O. (The figure is not drawn to scale.)

60. In circle O, mR = 43. Find mO. (The figure is not drawn to scale.)

Name: ________________________ ID: A

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61. Given that DAB and DCB are right angles and mBDC = 46º, what is m CAD? (The figure is not drawn to scale.)

62. If mACD 13, what is mABD?

Name: ________________________ ID: A

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63. BD

is tangent to circle O at C, mAEC 264, and mACE 91. Find mDCE.(The figure is not drawn to scale.)

64. AC

is tangent to circle O at A. If mBY 27, what is mYAC? (The figure is not drawn to scale.)

Name: ________________________ ID: A

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65. PQ

is tangent to the circle at C. In the circle, mAD 94, and mD = 83. Find mDCQ.

(The figure is not drawn to scale.)

66. PQ

is tangent to the circle at C. In the circle, mBC 75. Find mBCP.

(The figure is not drawn to scale.)

Name: ________________________ ID: A

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67. mS 21, mRS 80, and RU is tangent to the circle at R. Find mU.(The figure is not drawn to scale.)

68. mDE 113 and mBC 66. Find mA. (The figure is not drawn to scale.)

69. Find the value of x for mAB 23 and mCD 26. (The figure is not drawn to scale.)

Name: ________________________ ID: A

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70. DA is tangent to the circle at A and DC is tangent to the circle at C. Find mD for mB = 55. (The figure is not drawn to scale.)

71. A park maintenance person stands 16 m from a circular monument. Assume that her lines of sight form tangents to the monument and make an angle of 43°. What is the measure of the arc of the monument that her lines of sight intersect?

72. The lines in the figure are tangent to the circle at points A and B. Find the measure of value of AB for mP 56. (The figure is not drawn to scale.)

73. The farthest distance a satellite signal can directly reach is the length of the segment tangent to the curve of Earth’s surface. If the measure of the angle formed by the tangent satellite signals is 135, what is the measure of the intercepted arc on Earth? (The figure is not drawn to scale.)

Name: ________________________ ID: A

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74. A footbridge is in the shape of an arc of a circle. The bridge is 3.5 ft tall and 25 ft wide. What is the radius of the circle that contains the bridge? Round to the nearest tenth.

Find the value of x. If necessary, round your answer to the nearest tenth. The figures are not drawn to scale.

75.

76. AB = 10, BC = 7, and CD = 8

Name: ________________________ ID: A

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77. The figure consists of a chord, a secant, and a tangent to the circle. Round to the nearest hundredth, if necessary.

78. CD is tangent to circle O at D. Find the diameter of the circle for BC = 15 and DC = 24. Round to the nearest tenth.(The diagram is not drawn to scale.)

79. AD is tangent to circle O at D. Find AB. Round to the nearest tenth if necessary.

Write the standard equation for the circle.

80. center (–9, –2), r = 6

Name: ________________________ ID: A

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81. Find the center and radius of the circle with equation (x + 9)2 + (y – 10)2 = 16.

82. What is the equation of the circle with center (2, –2) that passes through the point (–10, 10)?

83. What is the equation of the circle with center (0, 0) that passes through the point (8, 3)?

84. A manufacturer is designing a two-wheeled cart that can maneuver through tight spaces. On one test model, the

wheel placement (center) and radius is modeled by the equation (x 0.5)2 (y 2)2 16. What is the graph

that shows the position and radius of the wheels?

85. Write the equation of the locus of all points in the coordinate plane 6 units from (–6, –4).

ID: A

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Geometry SIA #4, Review #2Answer Section

SHORT ANSWER

1. ANS: 39, 47

PTS: 1 DIF: L3 REF: 2-1 Patterns and Inductive ReasoningOBJ: 2-1.1 Use inductive reasoning to make conjectures STA: MA.912.G.8.4TOP: 2-1 Problem 1 Finding and Using a Pattern KEY: pattern | inductive reasoningDOK: DOK 2

2. ANS: 7

1024,

74096

PTS: 1 DIF: L3 REF: 2-1 Patterns and Inductive ReasoningOBJ: 2-1.1 Use inductive reasoning to make conjectures STA: MA.912.G.8.4TOP: 2-1 Problem 1 Finding and Using a Pattern KEY: pattern | inductive reasoningDOK: DOK 2

3. ANS:

The eleventh figure in the pattern is .

PTS: 1 DIF: L2 REF: 2-1 Patterns and Inductive ReasoningOBJ: 2-1.1 Use inductive reasoning to make conjectures STA: MA.912.G.8.4TOP: 2-1 Problem 2 Using Inductive Reasoning KEY: inductive reasoning | patternDOK: DOK 2

4. ANS: The twenty-fourth term is C.

PTS: 1 DIF: L3 REF: 2-1 Patterns and Inductive ReasoningOBJ: 2-1.1 Use inductive reasoning to make conjectures STA: MA.912.G.8.4TOP: 2-1 Problem 2 Using Inductive Reasoning KEY: inductive reasoning | patternDOK: DOK 2

5. ANS: The sum is 19 19 361.

PTS: 1 DIF: L4 REF: 2-1 Patterns and Inductive ReasoningOBJ: 2-1.1 Use inductive reasoning to make conjectures STA: MA.912.G.8.4TOP: 2-1 Problem 3 Collecting Information to Make a Conjecture KEY: inductive reasoning | conjecture | pattern DOK: DOK 3

ID: A

2

6. ANS: The sum is 15 16.

PTS: 1 DIF: L3 REF: 2-1 Patterns and Inductive ReasoningOBJ: 2-1.1 Use inductive reasoning to make conjectures STA: MA.912.G.8.4TOP: 2-1 Problem 3 Collecting Information to Make a Conjecture KEY: inductive reasoning | pattern | conjecture DOK: DOK 2

7. ANS: 51 words per minute

PTS: 1 DIF: L3 REF: 2-1 Patterns and Inductive ReasoningOBJ: 2-1.1 Use inductive reasoning to make conjectures STA: MA.912.G.8.4TOP: 2-1 Problem 4 Making a Prediction KEY: conjecture | inductive reasoning | word problem | problem solving DOK: DOK 2

8. ANS: 25

PTS: 1 DIF: L2 REF: 2-1 Patterns and Inductive ReasoningOBJ: 2-1.1 Use inductive reasoning to make conjectures STA: MA.912.G.8.4TOP: 2-1 Problem 5 Finding a Counterexample KEY: conjecture | counterexampleDOK: DOK 2

9. ANS: The number is divisible by 3.

PTS: 1 DIF: L3 REF: 2-2 Conditional StatementsOBJ: 2-2.1 Recognize conditional statements and their parts STA: MA.912.G.8.4TOP: 2-2 Problem 1 Identifying the Hypothesis and the Conclusion KEY: conditional statement | conclusion DOK: DOK 2

10. ANS: Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Tuesday.

PTS: 1 DIF: L3 REF: 2-2 Conditional StatementsOBJ: 2-2.1 Recognize conditional statements and their parts STA: MA.912.G.8.4TOP: 2-2 Problem 1 Identifying the Hypothesis and the Conclusion KEY: conditional statement | hypothesis | conclusion DOK: DOK 2

11. ANS: If a number is divisible by 2, then it is divisible by 6.

PTS: 1 DIF: L2 REF: 2-2 Conditional StatementsOBJ: 2-2.2 Write converses, inverses, and contrapositives of conditionals STA: MA.912.D.6.2| MA.912.D.6.3 TOP: 2-2 Problem 4 Writing and Finding Truth Values of Statements KEY: conditional statement | converse of a conditional DOK: DOK 2

ID: A

3

12. ANS: 9x – 4 = 59

PTS: 1 DIF: L4 REF: 2-4 Deductive ReasoningOBJ: 2-4.1 Use the Law of Detachment and the Law of Syllogism STA: MA.912.D.6.4 TOP: 2-4 Problem 1 Using the Law of DetachmentKEY: Law of Detachment | deductive reasoning DOK: DOK 3

13. ANS: mK = mL

PTS: 1 DIF: L3 REF: 2-4 Deductive ReasoningOBJ: 2-4.1 Use the Law of Detachment and the Law of Syllogism STA: MA.912.D.6.4 TOP: 2-4 Problem 1 Using the Law of DetachmentKEY: deductive reasoning | Law of Detachment DOK: DOK 2

14. ANS: not possible

PTS: 1 DIF: L3 REF: 2-4 Deductive ReasoningOBJ: 2-4.1 Use the Law of Detachment and the Law of Syllogism STA: MA.912.D.6.4 TOP: 2-4 Problem 1 Using the Law of DetachmentKEY: deductive reasoning | Law of Detachment DOK: DOK 2

15. ANS: If it is Friday, then Jason is happy.

PTS: 1 DIF: L3 REF: 2-4 Deductive ReasoningOBJ: 2-4.1 Use the Law of Detachment and the Law of Syllogism STA: MA.912.D.6.4 TOP: 2-4 Problem 2 Using the Law of SyllogismKEY: deductive reasoning | Law of Syllogism DOK: DOK 2

16. ANS: If two lines intersect and form right angles, then they intersect and form 90° angles.

PTS: 1 DIF: L3 REF: 2-4 Deductive ReasoningOBJ: 2-4.1 Use the Law of Detachment and the Law of Syllogism STA: MA.912.D.6.4 TOP: 2-4 Problem 2 Using the Law of SyllogismKEY: deductive reasoning | Law of Syllogism DOK: DOK 2

17. ANS: Josef is wearing his school colors.

PTS: 1 DIF: L4 REF: 2-4 Deductive ReasoningOBJ: 2-4.1 Use the Law of Detachment and the Law of Syllogism STA: MA.912.D.6.4 TOP: 2-4 Problem 3 Using the Laws of Syllogism and Detachment KEY: deductive reasoning | Law of Detachment | Law of Syllogism DOK: DOK 3

ID: A

4

18. ANS:

AB, BC , CD, and DA

PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: 10-6.1 Find the measures of central angles and arcs NAT: CC G.CO.1STA: MA.912.G.6.2| MA.912.G.6.4| MA.912.G.6.5 TOP: 10-6 Problem 1 Naming ArcsKEY: major arc | minor arc | semicircle DOK: DOK 1

19. ANS:

MNL, NPM , PLN , and LMP

PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: 10-6.1 Find the measures of central angles and arcs NAT: CC G.CO.1STA: MA.912.G.6.2| MA.912.G.6.4| MA.912.G.6.5 TOP: 10-6 Problem 1 Naming ArcsKEY: major arc | minor arc | semicircle DOK: DOK 1

20. ANS: 172

PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: 10-6.1 Find the measures of central angles and arcs NAT: CC G.CO.1STA: MA.912.G.6.2| MA.912.G.6.4| MA.912.G.6.5 TOP: 10-6 Problem 2 Finding the Measures of Arcs KEY: major arc | measure of an arc | arcDOK: DOK 1

21. ANS: 8.9 cm

PTS: 1 DIF: L2 REF: 10-6 Circles and Arcs OBJ: 10-6.2 Find the circumference and arc length NAT: CC G.CO.1STA: MA.912.G.6.2| MA.912.G.6.4| MA.912.G.6.5 TOP: 10-6 Problem 3 Finding a DistanceKEY: circumference | diameter DOK: DOK 2

22. ANS: 32 in.

PTS: 1 DIF: L2 REF: 10-6 Circles and Arcs OBJ: 10-6.2 Find the circumference and arc length NAT: CC G.CO.1STA: MA.912.G.6.2| MA.912.G.6.4| MA.912.G.6.5 TOP: 10-6 Problem 3 Finding a DistanceKEY: circumference | radius DOK: DOK 2

23. ANS: 38 cm; 19 cm; 10.6 cm

PTS: 1 DIF: L4 REF: 10-6 Circles and Arcs OBJ: 10-6.2 Find the circumference and arc length NAT: CC G.CO.1STA: MA.912.G.6.2| MA.912.G.6.4| MA.912.G.6.5 TOP: 10-6 Problem 4 Finding Arc LengthKEY: circumference | radius DOK: DOK 2

ID: A

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24. ANS: 6 m

PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: 10-6.2 Find the circumference and arc length NAT: CC G.CO.1STA: MA.912.G.6.2| MA.912.G.6.4| MA.912.G.6.5 TOP: 10-6 Problem 4 Finding Arc LengthKEY: arc | circumference DOK: DOK 2

25. ANS: 29.16 m2

PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and SectorsOBJ: 10-7.1 Find the areas of circles, sectors, and segments of circles NAT: CC G.C.5 STA: MA.912.G.2.7| MA.912.G.6.4| MA.912.G.6.5TOP: 10-7 Problem 1 Finding the Area of a Circle KEY: area of a circle | radiusDOK: DOK 2

26. ANS: 1.69 m2

PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and SectorsOBJ: 10-7.1 Find the areas of circles, sectors, and segments of circles NAT: CC G.C.5 STA: MA.912.G.2.7| MA.912.G.6.4| MA.912.G.6.5TOP: 10-7 Problem 1 Finding the Area of a Circle KEY: area of a circle | radiusDOK: DOK 2

27. ANS: 17.9 cm2

PTS: 1 DIF: L4 REF: 10-7 Areas of Circles and SectorsOBJ: 10-7.1 Find the areas of circles, sectors, and segments of circles NAT: CC G.C.5 STA: MA.912.G.2.7| MA.912.G.6.4| MA.912.G.6.5TOP: 10-7 Problem 1 Finding the Area of a Circle KEY: circumference | radius | diameter | area of a circle | word problem | problem solvingDOK: DOK 3

28. ANS: 57.7 in.2

PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and SectorsOBJ: 10-7.1 Find the areas of circles, sectors, and segments of circles NAT: CC G.C.5 STA: MA.912.G.2.7| MA.912.G.6.4| MA.912.G.6.5TOP: 10-7 Problem 2 Finding the Area of a Sector of a Circle KEY: sector | circle | areaDOK: DOK 2

29. ANS: 25.7 cm2

PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and SectorsOBJ: 10-7.1 Find the areas of circles, sectors, and segments of circles NAT: CC G.C.5 STA: MA.912.G.2.7| MA.912.G.6.4| MA.912.G.6.5TOP: 10-7 Problem 2 Finding the Area of a Sector of a Circle KEY: sector | circle | area | central angleDOK: DOK 2

ID: A

6

30. ANS:

110.25 220.5 cm2

PTS: 1 DIF: L2 REF: 10-7 Areas of Circles and SectorsOBJ: 10-7.1 Find the areas of circles, sectors, and segments of circles NAT: CC G.C.5 STA: MA.912.G.2.7| MA.912.G.6.4| MA.912.G.6.5TOP: 10-7 Problem 3 Finding the Area of a Segment of a Circle KEY: sector | circle | area | central angleDOK: DOK 2

31. ANS:

120 36 3

m2

PTS: 1 DIF: L4 REF: 10-7 Areas of Circles and SectorsOBJ: 10-7.1 Find the areas of circles, sectors, and segments of circles NAT: CC G.C.5 STA: MA.912.G.2.7| MA.912.G.6.4| MA.912.G.6.5TOP: 10-7 Problem 3 Finding the Area of a Segment of a Circle KEY: sector | circle | area | central angleDOK: DOK 2

32. ANS:

192 144 3

m2

PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and SectorsOBJ: 10-7.1 Find the areas of circles, sectors, and segments of circles NAT: CC G.C.5 STA: MA.912.G.2.7| MA.912.G.6.4| MA.912.G.6.5TOP: 10-7 Problem 3 Finding the Area of a Segment of a Circle KEY: sector | circle | area | central angleDOK: DOK 2

33. ANS: 45

PTS: 1 DIF: L4 REF: 10-8 Geometric ProbabilityOBJ: 10-8.1 Use segment and area models to find the probabilities of eventsSTA: MA.912.G.2.5| MA.912.G.6.1| MA.912.G.6.5 TOP: 10-8 Problem 1 Using Segments to Find Probability KEY: geometric probability | segmentDOK: DOK 1

34. ANS: 1760

PTS: 1 DIF: L3 REF: 10-8 Geometric ProbabilityOBJ: 10-8.1 Use segment and area models to find the probabilities of eventsSTA: MA.912.G.2.5| MA.912.G.6.1| MA.912.G.6.5 TOP: 10-8 Problem 2 Using Segments to Find Probability KEY: geometric probability | segment | word problem | problem solving DOK: DOK 2

ID: A

7

35. ANS: 56

PTS: 1 DIF: L4 REF: 10-8 Geometric ProbabilityOBJ: 10-8.1 Use segment and area models to find the probabilities of eventsSTA: MA.912.G.2.5| MA.912.G.6.1| MA.912.G.6.5 TOP: 10-8 Problem 2 Using Segments to Find Probability KEY: geometric probability | segment | word problem | problem solving DOK: DOK 2

36. ANS: 0.32

PTS: 1 DIF: L3 REF: 10-8 Geometric ProbabilityOBJ: 10-8.1 Use segment and area models to find the probabilities of eventsSTA: MA.912.G.2.5| MA.912.G.6.1| MA.912.G.6.5 TOP: 10-8 Problem 3 Using Area to Find Probability KEY: geometric probabilityDOK: DOK 2

37. ANS: 39

PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 1 Finding Angle Measures KEY: tangent to a circle | point of tangency | properties of tangents | central angleDOK: DOK 1

38. ANS: 78

PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 1 Finding Angle Measures KEY: tangent to a circle | point of tangency | angle measure | properties of tangents | central angleDOK: DOK 1

39. ANS: 41

PTS: 1 DIF: L4 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 1 Finding Angle Measures KEY: properties of tangents | tangent to a circle | Tangent Theorem DOK: DOK 2

ID: A

8

40. ANS: 36

PTS: 1 DIF: L4 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 1 Finding Angle Measures KEY: properties of tangents | tangent to a circle | Tangent Theorem DOK: DOK 2

41. ANS: 15

PTS: 1 DIF: L2 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 2 Finding DistanceKEY: tangent to a circle | point of tangency | properties of tangents | Pythagorean TheoremDOK: DOK 2

42. ANS: 8,460 miles

PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 2 Finding DistanceKEY: tangent to a circle | point of tangency | properties of tangents | Pythagorean TheoremDOK: DOK 2

43. ANS: 16.3

PTS: 1 DIF: L4 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 2 Finding DistanceKEY: tangent to a circle | point of tangency | properties of tangents | Pythagorean TheoremDOK: DOK 2

44. ANS: 2.3 inches

PTS: 1 DIF: L4 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 3 Finding a RadiusKEY: word problem | tangent to a circle | point of tangency | properties of tangents | right triangle | Pythagorean Theorem DOK: DOK 2

ID: A

9

45. ANS: 8.3

PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 3 Finding a RadiusKEY: tangent to a circle | point of tangency | properties of tangents | right triangle | Pythagorean TheoremDOK: DOK 2

46. ANS: 4

PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 5 Circles Inscribed in Polygons KEY: properties of tangents | tangent to a circle | pentagon DOK: DOK 2

47. ANS: 62

PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 5 Circles Inscribed in Polygons KEY: properties of tangents | tangent to a circle | triangle DOK: DOK 2

48. ANS: 5 ft

PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: 12-2.2 Use perpendicular bisectors to chords NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 2 Finding the Length of a Chord KEY: circle | radius | chord | congruent chords | bisected chords DOK: DOK 1

49. ANS: 40 in.

PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: 12-2.2 Use perpendicular bisectors to chords NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 2 Finding the Length of a Chord KEY: circle | radius | chord | congruent chords | bisected chords DOK: DOK 1

ID: A

10

50. ANS: 15

PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: 12-2.2 Use perpendicular bisectors to chords NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 3 Using Diameters and Chords KEY: bisected chords | circle | perpendicular | perpendicular bisector | Pythagorean TheoremDOK: DOK 2

51. ANS: 10

PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: 12-2.2 Use perpendicular bisectors to chords NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 3 Using Diameters and Chords KEY: bisected chords | circle | perpendicular | perpendicular bisector | Pythagorean TheoremDOK: DOK 2

52. ANS: 39

PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: 12-2.1 Use congruent chords, arcs, and central angles NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: arc | central angle | congruent arcsDOK: DOK 1

53. ANS: 14

PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: 12-2.1 Use congruent chords, arcs, and central angles NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: circle | radius | chord | congruent chords | right triangle | Pythagorean TheoremDOK: DOK 3

54. ANS: 148

PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: 12-2.1 Use congruent chords, arcs, and central angles NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: arc | chord-arc relationship | diameter | chord | perpendicular | angle measure | circle | right triangle | perpendicular bisector DOK: DOK 2

ID: A

11

55. ANS: 211

PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: 12-2.1 Use congruent chords, arcs, and central angles NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: arc | central angle | congruent arcs | arc measure | arc addition | diameterDOK: DOK 1

56. ANS: 41.4

PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: 12-2.2 Use perpendicular bisectors to chords NAT: CC G.C.2STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: bisected chords | circle | perpendicular | perpendicular bisector | Pythagorean TheoremDOK: DOK 2

57. ANS: 28

PTS: 1 DIF: L3 REF: 12-3 Inscribed Angles OBJ: 12-3.1 Find the measure of an inscribed angle NAT: CC G.C.2| CC G.C.4STA: MA.912.G.6.3| MA.912.G.6.4 TOP: 12-3 Problem 1 Using the Inscribed Angle TheoremKEY: circle | inscribed angle | intercepted arc | inscribed angle-arc relationshipDOK: DOK 1

58. ANS: 23.5

PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles OBJ: 12-3.1 Find the measure of an inscribed angle NAT: CC G.C.2| CC G.C.4STA: MA.912.G.6.3| MA.912.G.6.4 TOP: 12-3 Problem 1 Using the Inscribed Angle TheoremKEY: circle | inscribed angle | intercepted arc | inscribed angle-arc relationshipDOK: DOK 1

59. ANS: 59

PTS: 1 DIF: L4 REF: 12-3 Inscribed Angles OBJ: 12-3.1 Find the measure of an inscribed angle NAT: CC G.C.2| CC G.C.4STA: MA.912.G.6.3| MA.912.G.6.4 TOP: 12-3 Problem 1 Using the Inscribed Angle TheoremKEY: circle | inscribed angle | central angle | intercepted arc DOK: DOK 2

ID: A

12

60. ANS: 86

PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles OBJ: 12-3.1 Find the measure of an inscribed angle NAT: CC G.C.2| CC G.C.4STA: MA.912.G.6.3| MA.912.G.6.4 TOP: 12-3 Problem 2 Using Corollaries to Find Angle MeasuresKEY: circle | inscribed angle | intercepted arc | inscribed angle-arc relationshipDOK: DOK 1

61. ANS: 272

PTS: 1 DIF: L3 REF: 12-3 Inscribed Angles OBJ: 12-3.1 Find the measure of an inscribed angle NAT: CC G.C.2| CC G.C.4STA: MA.912.G.6.3| MA.912.G.6.4 TOP: 12-3 Problem 2 Using Corollaries to Find Angle MeasuresKEY: circle | inscribed angle | intercepted arc | inscribed angle-arc relationshipDOK: DOK 2

62. ANS: 13

PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles OBJ: 12-3.1 Find the measure of an inscribed angle NAT: CC G.C.2| CC G.C.4STA: MA.912.G.6.3| MA.912.G.6.4 TOP: 12-3 Problem 2 Using Corollaries to Find Angle MeasuresKEY: circle | inscribed angle | intercepted arc | inscribed angle-arc relationshipDOK: DOK 1

63. ANS: 41

PTS: 1 DIF: L3 REF: 12-3 Inscribed Angles OBJ: 12-3.2 Find the measure of an angle formed by a tangent and a chordNAT: CC G.C.2| CC G.C.4 STA: MA.912.G.6.3| MA.912.G.6.4TOP: 12-3 Problem 3 Using Arc Measure KEY: circle | inscribed angle | tangent-chord angle | intercepted arc DOK: DOK 2

64. ANS: 76.5

PTS: 1 DIF: L3 REF: 12-3 Inscribed Angles OBJ: 12-3.2 Find the measure of an angle formed by a tangent and a chordNAT: CC G.C.2| CC G.C.4 STA: MA.912.G.6.3| MA.912.G.6.4TOP: 12-3 Problem 3 Using Arc Measure KEY: circle | inscribed angle | tangent-chord angle | intercepted arc | arc measure | angle measureDOK: DOK 2

ID: A

13

65. ANS: 50

PTS: 1 DIF: L3 REF: 12-3 Inscribed Angles OBJ: 12-3.2 Find the measure of an angle formed by a tangent and a chordNAT: CC G.C.2| CC G.C.4 STA: MA.912.G.6.3| MA.912.G.6.4TOP: 12-3 Problem 3 Using Arc Measure KEY: circle | inscribed angle | tangent-chord angle | intercepted arc | arc measure | angle measureDOK: DOK 2

66. ANS: 37.5

PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles OBJ: 12-3.2 Find the measure of an angle formed by a tangent and a chordNAT: CC G.C.2| CC G.C.4 STA: MA.912.G.6.3| MA.912.G.6.4TOP: 12-3 Problem 3 Using Arc Measure KEY: circle | inscribed angle | tangent-chord angle | arc measure | angle measureDOK: DOK 1

67. ANS: 19

PTS: 1 DIF: L3 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.1 Find measures of angles formed by chords, secants, and tangentsNAT: CC G.C.2 STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4TOP: 12-4 Problem 1 Finding Angle Measures KEY: circle | chord | angle measure | arc measure | intersection on the circle | intersection outside the circleDOK: DOK 2

68. ANS: 23.5

PTS: 1 DIF: L3 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.1 Find measures of angles formed by chords, secants, and tangentsNAT: CC G.C.2 STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4TOP: 12-4 Problem 1 Finding Angle Measures KEY: circle | secant | angle measure | arc measure | intersection outside the circleDOK: DOK 1

69. ANS: 24.5

PTS: 1 DIF: L3 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.1 Find measures of angles formed by chords, secants, and tangentsNAT: CC G.C.2 STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4TOP: 12-4 Problem 1 Finding Angle Measures KEY: circle | secant | angle measure | arc measure | intersection inside the circleDOK: DOK 1

ID: A

14

70. ANS: 70

PTS: 1 DIF: L3 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.1 Find measures of angles formed by chords, secants, and tangentsNAT: CC G.C.2 STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4TOP: 12-4 Problem 1 Finding Angle Measures KEY: circle | chord | angle measure | arc measure | intersection on the circle | intersection outside the circleDOK: DOK 2

71. ANS: 137

PTS: 1 DIF: L3 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.1 Find measures of angles formed by chords, secants, and tangentsNAT: CC G.C.2 STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4TOP: 12-4 Problem 2 Finding an Arc Measure KEY: circle | angle measure | word problem | arc measure | intersection outside the circleDOK: DOK 2

72. ANS: 124

PTS: 1 DIF: L2 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.1 Find measures of angles formed by chords, secants, and tangentsNAT: CC G.C.2 STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4TOP: 12-4 Problem 2 Finding an Arc Measure KEY: circle | angle measure | word problem | arc measure | intersection outside the circleDOK: DOK 2

73. ANS: 45

PTS: 1 DIF: L4 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.1 Find measures of angles formed by chords, secants, and tangentsNAT: CC G.C.2 STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4TOP: 12-4 Problem 2 Finding an Arc Measure KEY: circle | angle measure | word problem | arc measure | intersection outside the circleDOK: DOK 2

74. ANS: 24.1 ft

PTS: 1 DIF: L4 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.2 Find the lengths of segments associated with circles STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4 TOP: 12-4 Problem 3 Finding Segment Lengths KEY: arc | radius | intersection inside the circle | chord | segment length | word problemDOK: DOK 3

ID: A

15

75. ANS: 20

PTS: 1 DIF: L3 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.2 Find the lengths of segments associated with circles STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4 TOP: 12-4 Problem 3 Finding Segment Lengths KEY: circle | chord | intersection inside the circle DOK: DOK 2

76. ANS: 6.88

PTS: 1 DIF: L3 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.2 Find the lengths of segments associated with circles STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4 TOP: 12-4 Problem 3 Finding Segment Lengths KEY: circle | intersection outside the circle | secant DOK: DOK 2

77. ANS: 12

PTS: 1 DIF: L4 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.2 Find the lengths of segments associated with circles STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4 TOP: 12-4 Problem 3 Finding Segment Lengths KEY: circle | chord | intersection inside the circle | intersection outside the circle | secant | tangent to a circleDOK: DOK 2

78. ANS: 23.4

PTS: 1 DIF: L3 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.2 Find the lengths of segments associated with circles STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4 TOP: 12-4 Problem 3 Finding Segment Lengths KEY: circle | intersection outside the circle | secant | tangent | diameter DOK: DOK 2

79. ANS: 7.1

PTS: 1 DIF: L3 REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.2 Find the lengths of segments associated with circles STA: MA.912.G.6.2| MA.912.G.6.3| MA.912.G.6.4 TOP: 12-4 Problem 3 Finding Segment Lengths KEY: circle | intersection outside the circle | secant | tangent DOK: DOK 2

ID: A

16

80. ANS:

(x + 9)2 + (y + 2)2 = 36

PTS: 1 DIF: L3 REF: 12-5 Circles in the Coordinate PlaneOBJ: 12-5.1 Write the equation of a circle NAT: CC G.GPE.1STA: MA.912.G.1.1| MA.912.G.6.6| MA.912.G.6.7 TOP: 12-5 Problem 1 Writing the Equation of a Circle KEY: equation of a circle | center | radiusDOK: DOK 1

81. ANS: center (–9, 10); r = 4

PTS: 1 DIF: L3 REF: 12-5 Circles in the Coordinate PlaneOBJ: 12-5.2 Find the center and radius of a circle NAT: CC G.GPE.1STA: MA.912.G.1.1| MA.912.G.6.6| MA.912.G.6.7 TOP: 12-5 Problem 1 Writing the Equation of a Circle KEY: center | circle | coordinate plane | radius DOK: DOK 2

82. ANS:

(x 2)2 (y (2))2 288

PTS: 1 DIF: L3 REF: 12-5 Circles in the Coordinate PlaneOBJ: 12-5.2 Find the center and radius of a circle NAT: CC G.GPE.1STA: MA.912.G.1.1| MA.912.G.6.6| MA.912.G.6.7 TOP: 12-5 Problem 2 Using the Center and a Point on a Circle KEY: equation of a circle | center | radius | point on the circle | algebra DOK: DOK 2

83. ANS:

x2 y2 73

PTS: 1 DIF: L3 REF: 12-5 Circles in the Coordinate PlaneOBJ: 12-5.2 Find the center and radius of a circle NAT: CC G.GPE.1STA: MA.912.G.1.1| MA.912.G.6.6| MA.912.G.6.7 TOP: 12-5 Problem 2 Using the Center and a Point on a Circle KEY: equation of a circle | center | radius | point on the circle | algebra DOK: DOK 2

ID: A

17

84. ANS:

PTS: 1 DIF: L3 REF: 12-5 Circles in the Coordinate PlaneOBJ: 12-5.2 Find the center and radius of a circle NAT: CC G.GPE.1STA: MA.912.G.1.1| MA.912.G.6.6| MA.912.G.6.7 TOP: 12-5 Problem 3 Graphing a Circle Given Its Equation KEY: equation of a circle | center | radius | point on the circle | algebra DOK: DOK 2

85. ANS:

(x + 6)2 + (y + 4)2 = 36

PTS: 1 DIF: L4 REF: 12-6 Locus: A Set of PointsOBJ: 12-6.1 Draw and describe a locus NAT: CC G.GMD.4 STA: MA.912.G.8.3 TOP: 12-6 Problem 1 Describing a Locus in a PlaneKEY: locus | equation of a circle DOK: DOK 2