Free Printable Circles with Lines, Arc Length & Sector Area, Degrees & Radians

1.

Solve for x.

a)

4

b)

6

c)

9

d)

7

2.

Solve for x

(a)

3.

Solve for x.

a)

10

b)

15

c)

7.5

d)

8

4.

Solve for x.

a)

18

b)

144

c)

12

d)

16

5.

Solve for x.

(a)

6.

Solve for x.

(a)

7.

Solve for x.

a)

12

b)

1.5

c)

1

d)

4

8.

Solve for x

(a)

9.

What is the measure of arc AB?

a)

140

b)

142

c)

180

d)

153

10.

What is the measure of arc WYZ?

a)

231

b)

255

c)

168

d)

200

11.

What is the measure of angle DEF?

a)

72

b)

73

c)

74

d)

75

12.

What is the measure of angle ABC?

a)

90

b)

180

c)

45

d)

80

13.

What is the measure of angle JML?

a)

93

b)

94

c)

95

d)

96

14.

What is the measure of angle HKI?

a)

72

b)

73

c)

74

d)

75

15.

What is the diameter?

a)

8

b)

16

c)

10

d)

4

16.

Which segment is a radius?

a)

LM

b)

DC

c)

BD

d)

ML

17.

Which segment is the diameter?

a)

AC

b)

BD

c)

LM

d)

CE

18.

what is the circumference of this circle ?

a)

3.14 cm

b)

37.68 cm

c)

24 cm

d)

68.4 cm

19.

What is the measure of ∠PTQ?

a)

100°

b)

140°

c)

180°

d)

120°

20.

If the measure of arc ABC = 210°, what is the measure of ∠AOC?

a)

150°

b)

100°

c)

210°

d)

105°

21.

Give an example of a chord

a)

line HI

b)

line KL

c)

line GH

d)

line GJ

22.

Give an example of a major arc

a)

arc JH

b)

arc HI

c)

arc JLH

d)

arc JL

23.

Find x

a)

10

b)

5

c)

18

d)

9

24.

opposite angles in any quadrilateral inscribed in a circle are __________ of each other.

a)

complements

b)

supplements

c)

congruent

d)

opposite

25.

One slice of pizza at PIE.ZAA in downtown Asheville has a radius of 14 inches and a central angle $45\degree$ . Which expression will find the sector area of the slice?

a)

$45\times\pi\times14$

b)

$\frac{45}{360}\times14^2$

c)

$\frac{45}{360}\times\pi\times14^2$

d)

$\pi\left(14\right)^2$

26.

Same slice....caculate the arc length given: $\frac{45}{360}\times2\pi\left(14\right)$

a)

5.5 inches

b)

11 inches

c)

88 inches

d)

154 inches

27.

What is the arc measure of the missing slice?

a)

$28\degree$

b)

$56\degree$

c)

$332\degree$

d)

$360\degree$

28.

What is the arc measure for an inscribed angle $40\degree$ ?

a)

$20\degree$

b)

$40\degree$

c)

$80\degree$

d)

$360\degree$

29.

Which formula is correct for finding x?

a)

$43+33=$

b)

$43+\frac{33}{2}=$

c)

$\frac{43+33}{2}=$

d)

$\frac{43-33}{2}=$

30.

Find the missing arc measure by solving $\frac{x-55}{2}=15$

a)

$20\degree$

b)

$30\degree$

c)

$35\degree$

d)

$85\degree$

31.

Which equation would solve for the arc measure x?

a)

$\frac{360-x-x}{2}=60$

b)

$\frac{360-x}{2}=60$

c)

$\frac{360-x+x}{2}=60$

d)

$360-x-x=30$

32.

Set up the equation for intersecting chords to find the value of a.

a)

$6+6=2+a$

b)

$6\times6=2\times a$

c)

$2\times6=a\times6$

d)

$66=2a$

33.

EXAMPLE: Find x.

a)

20

b)

$\sqrt[]{410}$

c)

49

d)

361

34.

YOU TRY: Find x.

a)

15

b)

300

c)

400

d)

20

35.

EXAMPLE: Find x.

a)

9

b)

144

c)

36

d)

81

36.

YOU TRY: Find x.

a)

16

b)

26

c)

576

d)

100

37.

How many degrees are in one revolution?

a)

$90\degree$

b)

$360\degree$

c)

180

38.

How many radians are in one revolution?

a)

$\pi$

b)

$\frac{\pi}{2}$

c)

$2\pi$

39.

How many radians are in $60\degree$ ?

a)

$\frac{\pi}{2}$

b)

$\frac{3\pi}{2}$

c)

$\frac{\pi}{3}$

40.

How many radians are in $45\degree$ ?

a)

$\pi$

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{4}$

41.

How many radians are in $135\degree$ ?

a)

$\pi$

b)

$\frac{3\pi}{4}$

c)

$\frac{4\pi}{3}$

42.

How many degrees are in $\frac{\pi}{4}$ radians?

a)

$30\degree$

b)

$45\degree$

c)

$60\degree$

43.

How many degrees are in $\frac{2\pi}{3}$ radians?

a)

$90\degree$

b)

$120\degree$

c)

$150\degree$

44.

How many degrees are in $\frac{5\pi}{4}$ radians?

a)

$270\degree$

b)

$225\degree$

c)

$180\degree$

45.

If you split a circle into 6 equal parts, how many degrees will each section be?

a)

30/pi^o

b)

60^o

c)

30^o

d)

60/pi^o

46.

How many radians does a circle have?

a)

360 degrees

b)

2pi radians

c)

pi radians

d)

^{2 radians}

47.

How many degrees does circle have?

a)

360 degrees

b)

2pi

c)

180 degrees

d)

pi

48.

How many radians are there in half a circle?

a)

2 pi

b)

180^o

c)

360^o

d)

pi

49.

How many degrees are there in half a circle?

a)

360^o

b)

2pi

c)

180^o

d)

pi

50.

What is π/3 radians in degrees?

a)

30

b)

60

c)

360

d)

90

51.

What is 11π/6 radians in degrees?

a)

30

b)

330

c)

360

d)

300

52.

What is 2π/3 radians in degrees?

a)

150

b)

120

c)

180

d)

30

53.

What is 120 degrees in radians?

a)

2π/3

b)

π/3

c)

5π/3

d)

4π/3

54.

What is 60 degrees in radians?

a)

2π/3

b)

π/3

c)

4π/3

d)

π/6

55.

What is 45 degrees in radians?

a)

π/2

b)

π/6

c)

π/4

d)

3π/4

56.

What is 150 degrees in radians?

a)

5π/6

b)

7π/6

c)

5π/4

d)

π/6

57.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

58.

What is 5π/6 radians in degrees?

a)

180

b)

150

c)

360

d)

120

59.

If a line is tangent to a circle, then it is perpendicular to the radius at its point of tangency.

a)

TRUE

b)

FALSE

60.

A tangent is a line that touches a circle at exactly two points.

a)

TRUE

b)

FALSE

61.

The measure of an angle formed by the intersection of two tangents on the exterior of the circle is half the sum of the measures of the major and minor arcs.

a)

TRUE

b)

FALSE

62.

The measure of an angle formed by the intersection of a secant and a tangent on the exterior of the circle is half the difference of the measures of their intercepted arcs.

a)

TRUE

b)

FALSE

63.

The measure of an angle formed by two secants intersecting at the exterior of the circle is equal to half the sum of the two intercepted arcs.

a)

TRUE

b)

FALSE

64.

Find the value of x.

a)

15

b)

18

c)

21

d)

28

65.

What is the measure of angle 2?

a)

40 degrees

b)

45 degrees

c)

80 degrees

d)

145 degrees

66.

∠ ABD is formed by a tangent and a secant intersecting outside of a circle. If minor arc AC = 72° and minor arc CD = 132° , what is the measure of ∠ ABD?

a)

$30\degree$

b)

$36\degree$

c)

$42\degree$

d)

$48\degree$

67.

If arc VY = 132° and ∠ YUV = 41° , what is the measure of arc XV?

a)

$35\degree$

b)

$40\degree$

c)

$45\degree$

d)

$50\degree$

68.

Given: $\overline{XY}=2x$ and $\overline{ZY}=6x-4$ are tangent to Circle A at Point X and Z. Find the value of x.

a)

1

b)

2

c)

3

d)

4

69.

Given: $\overline{XY}=2x\ and\ \overline{ZY}=6x-4$ are tangent to Circle A at Points X and Z. How long is $\overline{XY}?$

a)

1

b)

2

c)

3

d)

4

70.

If $m\angle ACE=81\degree$ , find measure of arc AC.

a)

$40.5\degree$

b)

$45.5\degree$

c)

$162\degree$

d)

$192\degree$

71.

If measure of arc ABC is 199 degrees, find $m\angle ACD.$

a)

$99.5\degree$

b)

$95.9\degree$

c)

$161\degree$

d)

$398\degree$

72.

If $m\angle IHO=53\degree$ and $arc\ CA=35\degree$ find $m\ arc\ OI.$

a)

$18\degree$

b)

$71\degree$

c)

$88\degree$

d)

$106\degree$

73.

If $m\ arc\ NA\ =19\degree$ and $m\ arc\ EY\ =\ 101\degree$ find $m\angle J.$

a)

$82\degree$

b)

$120\degree$

c)

$41\degree$

d)

$60\degree$

74.

Find the value of x

a)

4

b)

18

c)

3

d)

9

75.

Find the measure of angle ABD.

a)

14

b)

51

c)

37

d)

65

76.

What is the measure of angle 2?

a)

80

b)

45

c)

125

d)

40

77.

Find the value of x

a)

10

b)

15

c)

12

d)

19

78.

What is the value of x?

a)

22

b)

25

c)

15

d)

20

79.

QS is a tangent to circle P. Find QS.

a)

144

b)

14

c)

12

d)

13

80.

Find the value of x.

a)

12.5

b)

8

c)

35

d)

16

81.

Find the radius r

a)

2

b)

3

c)

4

d)

5

82.

Find the perimeter of the triangle.

a)

A

b)

B

c)

C

d)

D

83.

Given the following inscribed quadrilateral, what is the value of y?

a)

10

b)

20

c)

30

d)

40

84.

Find x. Assume that segments that appear to be tangent are tangent.

a)

2

b)

11

c)

7.6

d)

9

85.

What is the relationship between two tangents that share a common endpoint outside of the circle?

a)

One is half of the other.

b)

They are perpendicular.

c)

They are congruent.

d)

They are parallel.

86.

What is the relationship between an inscribed angle and its arc?

a)

The angle is half of the arc.

b)

The arc is half of the angle.

c)

They are congruent.

d)

The arc is smaller than the angle.

87.

What is the relationship between congruent chords and their arcs?

a)

The chord bisects the arc.

b)

The arc is half the length of the chord.

c)

The chord is half of the arc.

d)

They are congruent.

88.

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.

a)

25.2 in²

b)

28.5 in²

c)

31.4 in²

d)

38.2 in²

89.

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

90.

The distance along the edge of a circle between two points is the _________

a)

area of a sector

b)

arc length

c)

arc of a circle

d)

sector of a circle

91.

What is the area of the shaded SECTOR? Round to the nearest hundredth.

a)

9.42 u²

b)

113.10 u²

c)

284.3 u²

d)

452.39 u²

92.

If a quadrilateral is inscribed in a circle, then its ____angles are _____.

a)

adjacent; complimentary

b)

opposite; complimentary

c)

adjacent; supplementary

d)

opposite; supplementary

93.

If a quadrilateral is inscribed in a circle, what is the sum of its opposite angles?

a)

$90^\circ$ each

b)

$180^\circ$ each

c)

$360^\circ$ in total

94.

Quadrilateral ABCD is inscribed in the circle. If m∠ A = 95° , what also must be true?

a)

m∠B = 95°

b)

m∠C = 85°

c)

m∠D = 105°

d)

m∠D = 95°

95.

This is a picture of ___________.

a)

Major Arc

b)

Minor Arc

c)

Central Angle

d)

Inscribed Angle

96.

A quadrilateral ABCD is inscribed in circle O. What are the values of x and Y?

a)

X=180+107

Y=180-90

b)

X=180+90

Y=180+107

c)

X=180-107

Y=180-90

d)

X=180

Y=90

97.

What is the part of the circle highlighted in red called?

a)

semi-circle arc

b)

major arc

c)

minor arc

d)

sector

98.

Find the circumference of the circle.

a)

38.47 cm

b)

10.99 cm

c)

43.96 cm

d)

21.98 cm

99.

Find the diameter of the circle.

a)

5 units

b)

4 units

c)

12.2 units

d)

7.5 units

100.

What is this called?

a)

Chord

b)

Minor Arc

c)

Circumference

d)

Secant

101.

if m< CAB = 70° then m(arc CxA) = _____

a)

70⁰

b)

35⁰

c)

100⁰

d)

140⁰

102.

Find the measure of $\angle HFG$

a)

23

b)

44

c)

3

d)

48

103.

Solve for x.

a)

37.5

b)

11

c)

118

d)

15

Circles with Lines, Arc Length & Sector Area, Degrees & Radians

Total questions: 103

Worksheet time: 4hrs 59mins

Similar Resources on Wayground