Free Printable Geometry: Topic 10 (Circles)

1.

If the area of a circle is 25 π in² , then the diameter is?

a)

10 in

b)

5 in

c)

25 in

d)

pi in

2.

If the area of circle is 100 π , find the radius of the circle.

a)

10 π

b)

10

c)

50

d)

50 π

3.

Equal _____ of the congruent circles subtend equal angles at the centers.

a)

Segments

b)

Radii

c)

Arcs

d)

Chords

4.

If AB and CD are two chords of a circle intersecting at point E, as per the given figure. Then:

a)

∠BEQ > ∠CEQ

b)

∠BEQ = ∠CEQ

c)

∠BEQ < ∠CEQ

d)

None of the above

5.

In the below figure, the value of ∠ADC is:

a)

60⁰

b)

30⁰

c)

45⁰

d)

55⁰

6.

In the figure, O is the centre of the circle and PR = QR. What is the measure of ∠PQR?

a)

60⁰

b)

110⁰

c)

75⁰

d)

45⁰

7.

In the figure, O is the centre of the circle. What is the measure of ∠ACB?

a)

45⁰

b)

60⁰

c)

70⁰

d)

90⁰

8.

The region between an arc and the two radii, joining the centre to the endpoints of the arc is called a ————–

a)

Sector

b)

Segment

c)

Arc

d)

Area

9.

In the figure, if O is the centre of a circle, then the measure of ∠ACB is:

a)

80⁰

b)

100⁰

c)

40⁰

d)

60⁰

10.

Determine the measure of ∠NOP

a)

15°

b)

20°

c)

40°

d)

50°

11.

Determine the measure of ∠UVS

a)

19.5°

b)

39°

c)

78°

d)

102°

12.

Find the measure of arc NL

a)

21°

b)

42°

c)

45°

d)

84°

13.

Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.

a)

36

b)

35

c)

30

d)

41

14.

Can a secant be a tangent?

a)

yes they are both the same line

b)

yes they are both parts of a circle

c)

No secant intersects twice and tangent intersects once

d)

No they both have nothing to do with circles

15.

Find the measure of angle ABD.

a)

14

b)

51

c)

37

d)

65

16.

What is the measure of angle 2?

a)

80

b)

45

c)

125

d)

40

17.

Find the m∠MNQ.

a)

89⁰

b)

45⁰

c)

158⁰

d)

22⁰

18.

Find the measure of minor arc AV.

a)

55°

b)

115°

c)

85°

d)

95°

19.

a)

A

b)

B

c)

C

d)

D

20.

a)

A

b)

B

c)

C

d)

D

21.

Find the length of the bolded arc.

a)

$3.5\pi$ yd

b)

$7\pi$ yd

c)

$14\pi$ yd

d)

$90\pi$ yd

22.

Find the length of the bolded arc.

a)

14.28 mi

b)

21.86 mi

c)

93.4 mi

d)

29.75 mi

23.

Find the AREA of the bolded sector.

a)

$300.9\ mi^2$

b)

$401\ mi^2$

c)

$552.3\ mi^2$

d)

$602\ mi^2$

24.

What is the measure of angle x?

a)

67

b)

85

c)

92

d)

360

25.

What is 360° in radian?

a)

2π radian

b)

π radian

c)

π/4 radian

d)

π/2 radian

26.

What is 150° in radians?

a)

5π/6

b)

7π/6

c)

5π/4

d)

π/6

27.

What is 45° in radians?

a)

π/2

b)

π/6

c)

π/4

d)

3π/4

28.

What is 90° in radians?

a)

π/4 radian

b)

π/2 radian

c)

π/6 radian

d)

3π/2 radian

29.

What is 60 degrees in radians?

a)

2π/3

b)

π/3

c)

4π/3

d)

π/6

30.

What is 270 degrees in radians?

a)

π/4

b)

3π/2

c)

3π/4

d)

π/2

31.

Convert 100⁰ to radians

a)

5π/9

b)

π/2

c)

5π/8

d)

5π/6

32.

What is 2π/3 radians in degrees?

a)

150

b)

120

c)

180

d)

30

33.

What is 11π/6 radians in degrees?

a)

30

b)

330

c)

360

d)

300

34.

Find the arc length. Leave your answer in terms of π.

a)

7/4π

b)

7/2π

c)

1/8π

d)

45π

35.

Find the arc length of the bolded arc. Give your answer in terms of π.

a)

(65/12)π cm

b)

17.02 cm

c)

(845/24)π cm

d)

26π cm

36.

Alison is jogging on a circular track that has a radius of 140 feet. She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.

a)

47

b)

74

c)

94

d)

123

37.

Rob is trying to open a can. He wants to find the arc length the can opener needs to travel to open the can half way. The radius of the can is 1.5 inches.

a)

10 inches

b)

2 feet

c)

4.71 inches

d)

3.53 inches

38.

What is the circumference?

a)

48

b)

96

c)

24

d)

18

39.

When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees. What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

a)

40

b)

35

c)

55

d)

69

40.

FIND THE ARC LENGTH OF THE BOLDED ARC

a)

A

b)

B

c)

C

d)

D

41.

Find the length of the minor arc.

a)

$\frac{19}{9}\pi$ cm

b)

$\frac{38}{9}\pi$ cm

c)

$\frac{576}{19}\pi$ cm

d)

$\frac{31}{36}\pi$ cm

42.

Find the area of the shaded sector of the circle. Leave your answer in terms of π. Pro Tip: Find the angle for the yellow section FIRST.

a)

b)

c)

d)

43.

What is the green area called?

a)

sector

b)

segment

c)

arc

d)

section

44.

What is the ϴ called?

a)

sector

b)

segment

c)

arc

d)

central angle

45.

Calculate the area of the sector.

a)

9.2 sq. in.

b)

10.5 sq. in.

c)

31.4 sq. in.

d)

38.2 sq. in.

46.

Find the area of the sector formed by arc s. Notice: this angle is in radians.

a)

4.71

b)

9.4

c)

12.5

d)

3.14

47.

What is the area of the green shaded segment?

a)

18.3 cm²

b)

50.3 cm²

c)

169.1 cm²

d)

201.1 cm²

48.

What is the area of the red shaded segment?

a)

25 in²

b)

28.5 in²

c)

12.5 in²

d)

383.4 in²

49.

Find the value of x.

a)

10

b)

181

c)

34

d)

40

50.

Find the value of x.

a)

31,3

b)

8

c)

16.3

d)

-8

51.

Find the measure of Arc MN

a)

96

b)

114

c)

228

d)

48

52.

solve for the missing angle

a)

45 degrees

b)

90 degrees

c)

100 degrees

d)

not enough information to answer

53.

a)

10

b)

11

c)

12

d)

13

54.

Solve for x.

a)

3.6

b)

9.2

c)

11.5

d)

14.3

55.

a)

10.8

b)

11.1

c)

12.3

d)

9.6

56.

Find AC. (Do not include units.)

(a)

57.

Find the radius of the circle. Round to the nearest tenth.

(Do not include units.)

(a)

58.

Find RS.

(a)

59.

Find CD.

Round to the nearest hundredth.

(a)

60.

a)

A

b)

B

c)

C

d)

D

61.

a)

A

b)

B

c)

C

d)

D

62.

a)

A

b)

B

c)

C

d)

D

63.

What is m∠ACB?

a)

67.5°

b)

90°

c)

22.5°

d)

45°

64.

Find m∠PRQ.

a)

39°

b)

90°

c)

51°

d)

15°

65.

Find a and b.

a)

a=74 degrees
b=93 degrees

b)

a=93 degrees
b=74 degrees

c)

a=87 degrees
b=106 degrees

d)

a=106 degrees
b=87 degrees

66.

Determine the m∠RPU.

a)

A

b)

B

c)

C

d)

D

67.

The intercepted arc of an inscribed angle is ___________________ the measure of the inscribed angle.

a)

congruent to

b)

half

c)

double

d)

supplementary to

68.

Inscribed Angle: an angle with its vertex _____________ the circle and its sides _____________

a)

at the center of;
forming chords/secants.

b)

on;
forming chords/secants.

c)

outside;
forming tangents.

d)

on the circle;
forming a tangent and a chord/secant.

69.

What is the name for the distance around a circle?

a)

Diameter

b)

Radius

c)

Circumference

d)

Chord

70.

a)

A

b)

B

c)

C

d)

D

71.

Find a and b.

a)

a=74 degrees
b=93 degrees

b)

a=93 degrees
b=74 degrees

c)

a=87 degrees
b=106 degrees

d)

a=106 degrees
b=87 degrees

72.

a)

6

b)

8

c)

10

d)

5

73.

a)

8

b)

6

c)

9

d)

10

74.

a)

3

b)

5

c)

15

d)

12

75.

a)

25

b)

16

c)

4

d)

18

76.

a)

7

b)

2

c)

4

d)

5

77.

a)

33

b)

18

c)

46

d)

16

78.

In figure $\angle ACB=36^0$ , then $\angle AOB$ =

a)

$18^0$

b)

$36^0$

c)

$72^0$

d)

$108^0$

79.

In figure $\angle ACB$ + $\angle AOB$ = $120^0$ , then $\angle AOB=$

a)

$120^0$

b)

$60^0$

c)

$80^0$

d)

$180^0$

80.

If two concentric circles are radius 5 cm and 3 cm are drawn, then the length of the chord of the larger circle which touches the smaller circle is ____.

a)

8 cm

b)

4 cm

c)

10 cm

d)

12 cm

81.

Solve for x.

a)

10

b)

85

c)

170

d)

180

82.

a)

240

b)

230

c)

205

d)

255

83.

Solve for x.

a)

140

b)

89

c)

51

d)

38

84.

Find the measure of angle ADB.

a)

47.5

b)

85

c)

132.5

d)

180

Geometry: Topic 10 (Circles)

Total questions: 84

Worksheet time: 5hrs 49mins

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