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Circles Instructional

Total questions: 90

Worksheet time: 4hrs 44mins

Name
Class
Date
1.

The distance around a circle is

a)

Circumference

b)

Radius

c)

Center

d)

Central Angle

2.

A polygon whose vertices are on a circle and whose edges are within the circle

a)

inscribed angle

b)

inscribed polygon

c)

inscribed shape

d)

inscribed math

3.

Every point on a circle in the same distance from the

a)

edge

b)

middle

c)

center

d)

radius

4.

An angle whose vertex is on the circumference of a circle and whose sides include chords of the circle

a)

inscribed polygon

b)

inscribed angle

c)

central angle

d)

inscribed edge

5.

The distance across the circle, through its center

a)

Radius

b)

Radii

c)

Circumferene

d)

Diameter

6.

An angle whose vertex is the center of the circle

a)

Inscribed polygon

b)

central angle

c)

inscribed angle

d)

vertex angle

7.

The distance from a circle to its center

a)

Chord

b)

Central angle

c)

circumference

d)

radius

8.

Two or more circles with the same center

a)

Concentric circles

b)

Happy circles

c)

lots of circles

d)

center circles

9.

A portion of a circle and its interior bound by an arc and two radii

a)

Section

b)

Sector

c)

Piece of pie

d)

part of circle

10.

A segment between two points on a circle

a)

Line segment

b)

lines

c)

central angle

d)

Chord

11.
What is the part of the circle highlighted in red called?
a)
semi-circle arc
b)
major arc
c)
minor arc
d)
sector
12.
What is the part of the circle highlighted in red called?
a)
semi-circle arc
b)
major arc
c)
minor arc
d)
sector
13.
What is the part of the circle highlighted in red called?
a)
semi-circle arc
b)
major arc
c)
minor arc
d)
sector
14.
An angle whose vertex lies on the circle and whose sides are chords of the circle
a)
inscribed angle 
b)
central angle
c)
arc
d)
radius
15.
A chord is a segment that connects ___________
a)
the center to the endpoint
b)
to one point outside the circle
c)
a central angle
d)
2 endpoints of a circle
16.
A line that intersects a circle at exactly one point
a)
secant
b)
circle
c)
chord
d)
tangent
17.
An angle whose vertex is the center of a circle
a)
central angle
b)
inscribed angle
c)
minor arc
d)
major arc
18.
In the equation (x+2)2+(y-3)2=4, the radius of the circle is...
a)
4
b)
2
c)
3
d)
16
19.
What is the center and radius for a circle with the equation:
(x-4)2+(y+2)2=25
a)
C:(4, -2), r=5
b)
C:(-4, 2), r=5
c)
C:(4, -2), r=25
d)
C:(-4, 2), r=25
20.
What is the center of the circle with equation x2 + y2 = 1?
a)
(1, 1)
b)
(0, 0)
c)
not enough information
21.
What is the center of a circle with equation (x-4)2 + y2 = 5?
a)
(-4, 0)
b)
(4, 0)
c)
(4, 1)
d)
(-4, 1)
22.
Write the Standard Equation for a circle with a center (-2,5) and radius 7
a)
(x+2)2 + (y-5)2 = 49
b)
(x+9)2 + (y-6)2 = 49
c)
(x+2)2 + (y-5)2 = 32
23.
What is the equation of the circle?
a)
(x+1)2 + (y +1)2 = 3
b)
(x+1)2 + (y -1)2 = 3
c)
(x+1)2 + (y +1)2 = 9
d)
(x-1)2 + (y -1)2 = 9
24.

The equation of the circle is ( x - 8 )2 + ( y + 3 )2 = 9 . The center is

a)

( 8, -3 )

b)

( 8, 3 )

c)

( -8, -3 )

d)

( -8, 3 )

25.
a)

A

b)

B

c)

C

d)

D

26.
a)
A
b)
B
c)
C
d)
D
27.
Determine the measure of Arc BA.
a)
A
b)
B
c)
C
d)
D
28.
What is m∠ACB?
a)
67.5°
b)
90°
c)
22.5°
d)
45°
29.
Find the measure of <F
a)
46
b)
5
c)
90
d)
1.8
30.
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
31.

What is m < T

a)

m<T = 28.5 deg

b)

m< T = 180 deg

c)

m< T = 114 deg

d)

m< T = 90 deg

32.
Find the length of BC.
a)
2
b)
3
c)
9
d)
14
33.
a)
10
b)
15
c)
12
d)
19
34.
a)
14
b)
12
c)
19
d)
17
35.
A tangent line intersecting with a radius always creates a ____________ angle
a)
right
b)
acute
c)
obtuse
d)
straight
36.
Assume that all the lines that appear tangent are tangent. Find the perimeter
a)
54
b)
36
c)
48
d)
42
37.
Assume that all the lines that appear tangent are tangent. Find the perimeter
a)
54
b)
36
c)
48
d)
42
38.

Find angle x

a)

75 degrees

b)

85 degrees

c)

80 degrees

d)

78 degrees

39.
Find x
a)
10
b)
5
c)
18
d)
9
40.
Find the arc length.  Leave your answer in terms of π.
a)
7/4π
b)
7/2π
c)
1/8π
d)
45π
41.
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)
9.2 sq. in.
b)
10.5 sq. in.
c)
31.4 sq. in.
d)
38.2 sq. in.
42.
Which angles are congruent?
a)
<ACB = <ADB
b)
<ADB=<AEB
c)
<AEB=<ACB
d)
<ACB = <ADB = <AEB
43.
If a  quadrilateral is inscribed in a circle, then its ____angles are _____.
a)
adjacent; complimentary
b)
opposite; complimentary
c)
adjacent; supplementary
d)
opposite; supplementary
44.
Which angles are congruent?
a)
<ACB = <ADB
b)
<ADB=<AEB
c)
<AEB=<ACB
d)
<ACB = <ADB = <AEB
45.
A region bounded by an arc and its chord is a
a)
sector of a circle
b)
arc of a circle
c)
arc length of a circle
d)
segment of a circle
46.
Find the area of the dark blue sector shown at the left.  The radius of the circle is 4 units and the length of the arc (the curved edge of the sector) measures 7.85 units.  Express answer to thenearest tenth of a square unit.
a)
0.3 square units
b)
15.7 square units
c)
19.7 square units
d)
50.3 square units
47.
In circle O, the radius is 4, and the measure of minor arc AB is 120 degrees. Find the length of minor arc AB to the nearest integer.
a)
5
b)
9
c)
8
d)
6
48.
Stephanie is cutting a pie. Stephanie's mother wants one fourth of the pie. The diameter is 20 cm. What is the sector area of the pie her mother does not want?
a)
235.62 cm squared
b)
three fourths of the pie
c)
78.54 cm squared
d)
83.99 cm squared
49.

Give an example of a chord

a)

line HI

b)

line KL

c)

line GH

d)

line GJ

50.

Give an example of a major arc

a)

arc JH

b)

arc HI

c)

arc JLH

d)

arc JL

51.

Find the arc MEASURE of arc YU

a)

55˚

b)

125˚

c)

17˚

d)

25˚

52.

Find the arc measure for arc VW

a)

45˚

b)

25˚

c)

17˚

d)

55˚

53.

Find the value of X

a)

20

b)

6

c)

10

d)

4

54.

If TR is 11ft, find the length of arc PS

a)

24.54 ft

b)

31.49 ft

c)

37.43

d)

36.08 ft

55.

Find the arc measure for arc RQT

a)

335˚

b)

126˚

c)

224˚

d)

94˚

56.
Select the true statement.
a)
circumference is used when finding sector area
b)
circumference is used when finding arc measure
c)
circumference is used when finding arc length
d)
circumference has nothing to do with circles 
57.
Find the area of the shaded segment of circle O to the nearest tenth of a square unit.  The radius of the circle is 6 units.  The perpendicular from O to the chord joining point A to point B measures 4 units.
a)
4.8 sq. units
b)
30.3 sq. units
c)
12.4 sq. units
d)
48.2 sq. units
58.
What is the area of the shaded region? Round to the nearest hundredth.
a)
78.53
b)
314.16
c)
28.54
d)
58.54
59.
 Find AB and DE.
a)
15, 32
b)
32, 15
c)
32, 24
d)
15, 24
60.
Solve for x.
a)
4.2
b)
6.6
c)
10.4
d)
11.6
61.
Find the m∠HFG.
a)
61⁰
b)
65⁰
c)
57⁰
d)
244⁰
62.
Solve for x.  Round to the nearest degree.
a)
140⁰
b)
89⁰
c)
76⁰
d)
38⁰
63.
Find the m∠1.
a)
130⁰
b)
65⁰
c)
44⁰
d)
86⁰
64.
Find the m∠2.
a)
80⁰
b)
45⁰
c)
125⁰
d)
40⁰
65.
Solve for x and y.
a)
x=85⁰  y = 150⁰
b)
x = 85⁰  y = 50⁰
c)
x = 95⁰   y = 150⁰
d)
x = 95⁰   y = 50⁰
66.
Find m∠R.
a)
24⁰
b)
41⁰
c)
67⁰
d)
139⁰
67.
Find x.
a)
29⁰
b)
33⁰
c)
41.5⁰
d)
50⁰
68.
To find an angle inside the circle you use which of the following.
a)
(1/2)arc
b)
 (1/2)(arc+arc)
c)
(1/2)(arc - arc)
d)
I don't know
69.
Conclusion?
a)
The measure of angle ABC is half of arc AB
b)
The measure of arc AB is half of Angle ABC
c)
The measure of angle ABC is double of arc AB
d)
The measure of arc AB is congruent to Angle ABC
70.
To find an angle outside the circle you use which of the following.
a)
(1/2)arc
b)
(1/2)(arc+arc)
c)
(1/2)(arc-arc)
d)
I don't know
71.
To find an angle on the circle you use which of the following.
a)
(1/2)arc
b)
(1/2)(arc+arc)
c)
(1/2)(arc-arc)
d)
I don't know
72.
What can you conclude?
a)
AB and AC are not congruent.
b)
AB= half of AC
c)
AC = half of AB
d)
AB=AC
73.
Solve for x.
a)
x = 35.67
b)
x = -1
c)
x = 14
d)
x = -4.33
74.
Solve for x.
a)
6
b)
8
c)
10
d)
12
75.

Solve for d.

a)

8

b)

9

c)

10

d)

12

76.
Solve for the value of x
a)
49
b)
10.6
c)
7
d)
112
77.

What is the relationship between ∠O and ∠P?

a)

∠O = 2∠P

b)

∠O = ½∠P

c)

∠O = ∠P

d)

∠O = 90° and ∠P = 45°

78.
Find the value of x.
a)
x = 17
b)
x = 16
c)
x = 29.67
d)
x = 18
79.
What is the measure of ∠PTQ?
a)
100°
b)
140°
c)
180°
d)
120°
80.
Name a chord.
a)
Segment XC
b)
Segment KM
c)
Segment FG
d)
LINE BD
81.

Name a secant.

a)

Segment XC

b)

Line LM

c)

Segment FG

d)

LINE BD

82.
Which number best represents an inscribed angle?
a)
1
b)
2
c)
8
d)
9
83.
Which number best represents an intercepted arc?
a)
1
b)
2
c)
6
d)
9
84.

What is the area of the shaded segment to the nearest tenth?

a)

5.6

b)

9.1

c)

13.3

d)

9.8

85.
Solve for x.
a)
6
b)
8
c)
10
d)
12
86.
What is the value of x?
a)
18
b)
8
c)
10
d)
30
87.

Circumscribed angle: an angle with its vertex _____________ the circle

a)

at the center of

b)

on

c)

outside

d)

inside

88.
Find x.
a)
9
b)
1
c)
27
d)
None of these
89.
Find the perimeter
a)
48.8
b)
47.4
c)
39.8
d)
36.4
90.
What can you conclude from the picture?
a)
m is parallel to circle C
b)
m is skew to circle C
c)
m bisects circle C
d)
m is tangent to circle C

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