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# Analytical geometry questions and answers pdf

150 Analytical Geometry Questions

Analytic Geometry A Accelerated Week 4 Page 39 of 53

Analytic Geometry A – Accelerated Week 4

Lesson 3.1 Special Lines and Segments with Circles

Lesson 3.2 Central Angles and Arc Measures

Lesson 3.3 Angles with a Vertex on the Circle and Arc Measures

Lesson 3.4 Other Angle Relationships with Circles

Lesson 3.5 Arcs and Chords

Lesson 3.6 Inscribed and Circumscribed Polygons

Lesson 3.7 Theorems of Inscribed Triangles and Quadrilaterals

Lesson 3.8 Circumference of a Circle

Lesson 3.9 Length of an Arc

Lesson 3.10 Area of a Circle

Lesson 3.11 Area of a Sector

Before working the problems, study the lesson listed above each problem set. Record the answers on the answer sheet. Turn in the answer sheet to be graded. For some problem sets, answer boxes are given. Choices may be used more than once if necessary. Lesson 3.1 Special Lines and Segments with Circles

Given the diagram, match the notation for the term that best describes it.

1. F 2.

3. 4.

5. 6. G

7. 8.

9. D 10.

Choices for 1‐10:

A) Chord

B) Tangent

D) Secant

E) Center

AB) Point of tangency

AC) Diameter

Analytic Geometry A Accelerated Week 4 Page 40 of 53

Draw the common tangents for the pairs of circles. Indicate how many common tangents

there are for each pair.

11. 12. 13. 14.

is a radius of ⊙C and is tangent to ⊙C. Find the value of x.

15. 16.

K and M are points of tangency. Find the value of x.

17. 18.

Choices for 11‐14:

A) 0 B) 1 C) 2 D) 3 E) 4 AB) 5 AC) 6

Choices for 15‐16:

A) 16 B) 24 C) 28 D) 32 E) 36 AB) 40 AC) 42 AD) 48 AE) 56 BC) 64

Choices for 17‐18:

A) 1 B) 2 C) 3 D) 4 E) 5 AB) 6 AC) 7 AD) 8 AE) 9 BC) 10

Analytic Geometry A Accelerated Week 4 Page 41 of 53

Lesson 3.2 Central Angles and Arc Measures

is a diameter in ⊙E. Identify the given arc as a major arc, minor arc, or semicircle.

A) Major arc B) Minor Arc C) Semicircle

19. 20. 21. 22.

23. 24. 25. 26.

and are diameters of ⊙U. Find the measure of the indicated arc.

27. 28.

29. 30.

31. 32.

33. 34.

35. 36.

Lesson 3.3 Angles with a Vertex on the Circle and Arc Measures

Find the indicated measure.

37. 38. 39.

Choices for 27‐36:

A) 42° B) 64° C) 74° D) 84° E) 106° AB) 116° AC) 138° AD) 180°

AE) 222° BC) 244° BD) 254° BE) 264° CD) 276° CE) 286° DE) 296° ABC) 318°

Choices for 37‐39:

A) 16° B) 18.5° C) 20° D) 32° E) 37° AB) 40° AC) 54° AD) 58°

AE) 64° BC) 74° BD) 80° BE) 119° CD) 122° CE) 126° DE) 149.5° ABC) 153°

Analytic Geometry A Accelerated Week 4 Page 42 of 53

40. 41.

42. 43.

44. 45.

46. 47.

Find the indicated measure.

48. ∠1 51. m(arc 1)

49. m(arc 2) 52. m(arc 2)

50. ∠3 53. ∠3

Choices for 40‐47:

A) 29° B) 42° C) 45° D) 48° E) 52° AB) 56° AC) 58°

AD) 64° AE) 84° BC) 90° BD) 96° BE) 106° CD) 116° CE) 180°

3

3 2

Choices for 48‐53:

A) 82° B) 86° C) 90° D) 92° E) 94° AB) 96° AC) 98°

AD) 164° AE) 168° BC) 172° BD) 180° BE) 188° CD) 192° CE) 196°

Analytic Geometry A Accelerated Week 4 Page 43 of 53

Lesson 3.4 Other Angle Relationships with Circles

Find ∠ .

54. 55. 56.

57. 58.

Find the value of x.

59. 60. 61.

Choices for 59‐61:

A) 7 B) 10 C) 12 D) 16 E) 18 AB) 24 AC) 26

AD) 32 AE) 58 BC) 61 BD) 63 BE) 67 CD) 70 CE) 76

Choices for 54‐58:

A) 22° B) 24° C) 26° D) 35° E) 37°

AB) 41° AC) 42° AD) 59.5° AE) 63° BC) 69°

BD) 72° BE) 94° CD) 109° CE) 112° ABC) 117°

ABD) 121.5° ABE) 128° BCD) 133° BCE) 142° CDE) 218°

Analytic Geometry A Accelerated Week 4 Page 44 of 53

Lesson 3.5 Arcs and Chords

Use the figure and to complete the statement.

62. ≅ _______ 63. ≅ ______ 64. ≅ _______

65. ≅ _______

66. ≅ _______

Find the measure of the indicated arc or chord.

67. 68. 69.

70. 71. 72.

E

F

Choices for 62‐66:

A) B) C) D)

AE) BC) BD) BE)

Choices for 67‐72: (Answers are in degrees when necessary.)

A) 7 B) 11 C) 22 D) 40 E) 45 AB) 50

AC) 58 AD) 64 AE) 65 BC) 80 BD) 90 BE) 104

CD) 115 CE) 116 DE) 122 ABC) 130 ABD) 140 ABE) 180

Analytic Geometry A Accelerated Week 4 Page 45 of 53

73. 74. 75.

76. 77.

Find the value of x.

78. 79. 80.

Choices for 73‐77:

A) 38° B) 48° C) 50° D) 57° E) 60° AB) 64°

AC) 65° AD) 66° AE) 70° BC) 74° BD) 85° BE) 90°

CD) 100° CE) 105° DE) 106° ABC) 112.5° ABD) 120° ABE) 135°

Choices for 78‐80:

A) 1 B) 3 C) 4 D) 6

E) 8 AB) 9 AC) 10 AD) 12

Analytic Geometry A Accelerated Week 4 Page 46 of 53

Choices for 81‐83:

A. inscribed polygon B. circumscribed polygon C. neither

Choices for 84‐86:

A. inscribed circle B. circumscribed circle C. neither

Lesson 3.6 Inscribed and Circumscribed Polygons

Identify the polygon as inscribed, circumscribed, or neither.

81. 82. 83.

Identify the circle as inscribed, circumscribed, or neither.

84. 85. 86.

Lesson 3.7 Theorems of Inscribed Triangles and Quadrilaterals

87. Draw . What term best describes ?

A) tangent

C) diameter

D) inscribed angle

E) center

Analytic Geometry A Accelerated Week 4 Page 47 of 53

Find the indicated measure.

88. 89. ∠

90. ∠

Use the given circle to find the following.

91. Solve for x. 95. Find ∠ .

92. Solve for y. 96. Find ∠ .

93. Find ∠ . 97. Solve for x.

94. Find ∠ . 98. Solve for y.

99. Find ∠ .

Choices for 88‐90:

A) 26° B) 30° C) 36° D) 40° E) 50°

AB) 54° AC) 60° AD) 64° AE) 74° BC) 90°

Choices for 91‐99: (Answers are in degrees when necessary.)

A) 14 B) 16 C) 21 D) 22 E) 29

AB) 32 AC) 38 AD) 39 AE) 52 BC) 56

BD) 58 BE) 63 CD) 64 CE) 65 DE) 70

ABC) 76 ABD) 78 ABE) 82 BCD) 98 BCE) 104

CDE) 110 ABCD) 112 ABCE) 115 BCDE) 116 ABCDE) 117

Analytic Geometry A Accelerated Week 4 Page 48 of 53

Lesson 3.8 Circumference of a Circle

Find the exact circumference of the circle.

100. 101.

102. 103.

Use a calculator to find the approximate circumference of the circle. Round the answer to the

hundredths.

104. 105. 106. 107.

108. 109.

Choices for 100‐103: (units of

measurement are not shown)

A) 20π B) 3.5π

C) 9π D) 14π

E) 2.25π AB) 7π

AE) 8π BC) 10.8π

BD) 6.5π BE) 16π

CD) 21.6π CE) 10π

Choices for 104‐107: (units of measurement are not shown)

A) 11 B) 7.07 C) 62.83 D) 31.42 E) 12.57 AB) 43.98 AC) 50.27

AD) 25.13 AE) 28.27 BC) 67.86 BD) 21.99 BE) 20.42 CD) 33.93 CE) 40.84

Choices for 108‐109: (units of

measurement are not shown)

A) 11.14 B) 21

C) 5.57 D) 2.79

E) 10.50 AB) 7.64

AE) 3.82 BC) 12.48

Analytic Geometry A Accelerated Week 4 Page 49 of 53

Find the indicated information for the circle. Round your answer to the hundredths.

110. Find the diameter of circle with a circumference of 43.25 ft.

111. Find the circumference of a circle with a diameter of 24 in.

112. Find the radius of a circle with a circumference of 0.36 m.

113. Find the diameter of a circle with a circumference of 56 cm.

Tire A tire has a diameter of 14 inches. Find the indicated information.

114. Find the circumference of the tire.

A) 21.99 in B) 43.98 in C) 87.96 in D) 28 in E) 7 in

115. How many feet will the tire travel in 18 revolutions?

A) 131.94 ft B) 42 ft C) 32.99 ft D) 126 ft E) 65.97 ft

116.

A) 450 cm B) 707 cm C) 481 cm D) 1414 cm E) 942 cm

Lesson 3.9 Length of an Arc

Round to the hundredths.

117. 118. 119.

Choices for 110‐113: (units of

measurement are not shown)

A) 0.11 B) 7.64 C) 8.91

D) 13.77 E) 0.06 AB) 21.63

AC) 6.88 AD) 28 AE) 75.40

BC) 17.83 BD) 37.70 BE) 0.18

Choices for 117–119: (units of measurement are not shown)

A) 3.14 B) 5.36 C) 6.28 D) 7.33 E) 8.56 AB) 12.43

AC) 30.24 AD) 32.68 AE) 34.94 BC) 35.94 BD) 36.02 BE) 38.92

CD) 40.54 CE) 42.84 DE) 44.04 ABC) 45.27 ABD) 46.63 ABE) 47.12

Analytic Geometry A Accelerated Week 4 Page 50 of 53

Round to the hundredths when necessary.

120. 121.

122. 123.

124. 125.

Given the length of an arc, find the indicated measure. Round to the hundredths.

126. 127. 128.

129.

A) 39.10 in

B) 42.56 in

C) 43.02 in

D) 44.12 in

C) 46.56 in

Choices for 120–125:

A) 80° B) 100° C) 160° D) 180° E) 200° AB)260°

AC) 280° AD) 340° AE) 9.77 m BC) 12.22 m BD) 19.55 m BE) 21.99 m

CD) 22.86 m CE) 24.43 m DE) 28.07 m ABC) 31.76 m ABD) 34.21 m ABE) 41.54 m

Choices for 126–128:

A) 65.98° B) 114.02° C) 122.42° D) 128.03° E) 52.48 ft AB) 56.92 ft

AC) 58.03 ft AD) 60.04 ft AE) 14.83 cm BC) 16.24 cm BD) 18.95 cm BE) 20.53 cm

Analytic Geometry A Accelerated Week 4 Page 51 of 53

Lesson 3.10 Area of a Circle

Find the exact area of the circle.

130. 131.

132. 133.

Use a calculator to find the approximate area of the circle. Round the answer to the

hundredths.

134. 135. 136. 137.

Find the indicated information for the circle.

138. Find the radius of a circle with an area of 64.25 ft 2 .

139. Find the diameter of a circle with an area of 24.56 in 2 .

140. Find the area of a circle with a circumference of 10.36 m.

141.

A) 263.89 ft 2 B) 441 ft

2 C) 1385.44 ft

2 D) 1764 ft

2 E) 5541.77 ft

2

Choices for 130‐133: (units of

measurement are not shown)

A) 100π B) 400π

C) 49π D) 14π

E) 64π AB) 42.25π

AE) 256π BC) 40π

BD) 169π BE) 20.25π

CD) 466.56π CE) 116.64π

Choices for 134‐137: (units of measurement are not shown)

A) 100.53 B) 201.06 C) 804.25 D) 135.72 E) 297.86 AB) 43.98 AC) 524.31

AD) 681.32 AE) 366.44 BC) 67.86 BD) 50.27 BE) 68.01 CD) 1465.74 CE) 153.94

Choices for 138‐140: (units of

measurement are not shown)

A) 2.80 B) 4.52

C) 5.59 D) 8.54

E) 10.23 AB) 12.65

Analytic Geometry A Accelerated Week 4 Page 52 of 53

Lesson 3.11 Area of a Sector

Find the area of the shaded sector. Round to the hundredths.

142. 143.

144. 145.

146. Find the area of a sector bound by a 32 ft radius and a central angle of 75°.

Given the area of the shaded sector, find the indicated measure. Round to the hundredths.

147. 148. 149.

Choices for 63–68: (units of measurement are not shown)

A) 6.83 B) 6.89 C) 6.96 D) 11.50 E) 11.83 AB) 12.02

AC) 106.88 AD) 107.06 AE) 108.22 BC) 221.07 BD) 222.46 BE) 223.88

Choices for 142‐146: (units of measurement are not shown)

A) 6.84 B) 9.08 C) 10.12 D) 16.08 E) 21.21 AB) 24.22

AC) 33.51 AD) 36.92 AE) 112.04 BC) 157.28 BD) 166.72 BE) 408.08

CD) 426.94 CE) 461.20 DE) 670.21 ABC) 812.42 ABD) 827.02 ABE) 846.83

Analytic Geometry A Accelerated Week 4 Page 53 of 53

150. Landscaping The diagram shows the area of a lawn covered by the sprinkler. What is the

area of the lawn that is covered by the sprinkler?

A) 285.88 ft 2

B) 296.15 ft 2

C) 298.65 ft 2

D) 301.59 ft 2

E) 308.32 ft 2

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