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Name:
Name _________________________________________ Period ____9/29 – 10/7/08GL
Name:
Period
GL
Unit 16: Cirlces
222
()()
xhykr
-+-=
I can define, identify and illustrate the following terms:
Interior of a circle
Exterior of a circle
Chord
Secant of a circle
Tangent to a circle
Point of tangency
Arc
Major Arc
Minor Arc
Arc Length
Inscribed Angle
Central angle of a circle
Semicircle
Sector of a circle
Segment in a circle
Concentric Circles
Circumscribed
(
)
(
)
22
7581
xy
-++=
Dates, assignments, and quizzes subject to change without advance notice.
Monday
Tuesday
Block Day
Friday
11/12
Introduction to Circles Computer Lab
13
Inscribed Angles
16
Interior and Exterior Angles
17
Mixed Angles
18/19
Quiz
Complex Angles
20
Review
23
TEST: Circles
Block Day, 5/11-12/11
Introduction to circles
· I can use and apply the equation of a circle
· Use the properties of tangents and chords to solve problems
· Find areas of sectors and segments
PRACTICE: Introduction to Circles Worksheet
COMPUTER LAB
Friday, 5/13/11
Inscribed Angles
· I can find the measure of an angle associated with a circle
· Apply the properties of arcs
PRACTICE: Inscribed Angles Worksheet
Monday, 5/16/11
Interior and Exterior Angles
· I can find the measure of an angle associated with a circle
· Apply the properties of arcs
PRACTICE: Interior and Exterior Angles Worksheet
Tuesday, 5/17/11
Mixed Angles
· I can find the measure of an angle associated with a circle
· Apply the properties of arcs
PRACTICE: Mixed Angles Worksheet
Block Day, 5/18-19/11
Complex Angles
· I can find the measure of an angle associated with a circle
· Apply the properties of arcs
PRACTICE: Complex Angles Worksheet
QUIZ: Circles
Friday, 5/20/11
REVIEW
· I can assess my strengths and weaknesses on all previously learned material.
PRACTICE: Review Activity/Worksheet
Monday, 5/16/11
(Test Unit #16: Circles
· I can demonstrate my ability on all previously learned material.
Day
Problem 1
Problem 2
Block
5/11-12
»
¼
»
»
»
6.
7.
8.
9.
10.
mCE
mCFE
mDC
mFG
mED
Find the length of
»
CA
.
¼
»
¼
mAKD
mABC
mDKB
mCE
mACE
S
S
Find the area of the shaded region
Friday
5/13
Given
22
(3)(5)16
xy
-++=
what is the center and the radius of the circle?
»
»
»
mBC
mBKC
mAKE
mED
mCD
S
S
»
»
»
________
_______
______
______
mBC
mBOA
mAB
mDF
=
=
=
=
R
AD
and
FC
are diameters,
42
mFGA
=
o
S
,
GA
is an angle bisector of
EGB
S
, and
»
27
mEF
=
o
. Find all the central angle measurements.
Monday
5/16
»
¼
_____
______
______
mEB
mECB
mA
=
=
=
R
Find x.
»
»
»
______
______
_____
______
mAGE
mAF
mAD
mCD
=
=
=
=
R
Find x.
Tuesday
5/17
»
»
______
______
______
mC
mED
mBC
=
=
=
R
Find x.
Find m
Block
5/18-19
Given a circle centered at (2, 9) with a radius of 9 write the equation.
C
B
A
Find x
Friday
5/20
a =_____ b=_____
G
F
C
B
E
A
D
Find x
Equation of a Circle
28
x
Notes
where (h, k) is the _____________ and r is the __________
EXAMPLE:
x
300
1. What is the center and radius of the following circle?2. Write the equation for the following circle.
x170
122
Center = ____________
Radius = ___________
3. Given a radius of (-2, 12) and a radius of 11 write the equation of the circle.
Central Angle Notes
The measure of a central angle is ____________ the measure or the intercepted arc created by the angle.
The total number of degrees in a circle is _____________.
The total number of degrees in a semicircle is _________.
Together we will answer the following questions.
Use the picture below for the example questions. Tell whether each arc is a major arc, minor arc, or a semi-circle. Then, find the degree measure of each arc. BD is a diameter and CD is an angle bisector.
6
54
A
Ex 1:
»
mAB
Ex 2:
»
mAF
Ex 3:
»
mBE
Ex 4:
¼
mFBE
Ex 5:
»
mBD
Ex 6:
»
mFD
Ex 7:
¼
mDAE
Introduction to Circles Worksheet
I. Use the picture at the right to answer the following questions.
x112
6
1. Diameter ________
2. Radius ________
3. Chord ________
4. Tangent ________
5. Minor Arc ________
6. Major Arc ________
7. Interior Point ________
8. Point on the Circle ________
9. Exterior Point ________
10. Center Point ________
11. Central Angle ________
12. Inscribed Angle ________
13. Interior Angle ________
14. Exterior Angle ________
b
165
106
a
II. Use the picture below for questions 1-10.
CF
is a diameter and
AE
is an angle bisector. Find the degree measure of each arc and then tell whether each arc is a major arc, minor arc, or a semi-circle.
20
x
»
»
»
»
¼
1.
2.
3.
4.
5.
mCB
mCG
mDF
mCF
mDFB
III. Use the picture below to answer questions 11 -20.
AC
and
BE
are diameters of the circle.
80
126
E
B
F
O
A
C
D
5
90
A
C
G
F
D
E
B
40
100
K
A
C
B
E
D
11.
16.
12.
17.
13.
18.
14.
19.
15.
20.
III. Find the center and radius from each equation.
21.
(
)
(
)
22
12516
xy
++-=
22.
(
)
2
2
225
xy
-+=
23.
22
4
xy
+=
24.
(
)
(
)
22
61349
xy
-+-=
»
»
»
mBC
mBKC
mAKE
mED
mCD
S
S
IV.
7.8.
9.
10.
The relationship between an inscribed angle and its intercepted arc can be written two ways:
Angle measure = ______________ OR Arc measure = _______________
EXAMPLES:
»
¼
»
»
»
6.
7.
8.
9.
10.
mCE
mCFE
mDC
mFG
mED
1:
»
mJK
=_________
2:
mGHI
R
=_________
¼
»
¼
mAKD
mABC
mDKB
mCE
mACE
S
S
222
()()
xhykr
-+-=
3:
mMAN
R
=_________
4:
mABP
R
=_________
5.
mCAB
R
=_________
6.
»
_____
mCB
=
,
_____
mCDB
=
S
(
)
(
)
22
7581
xy
-++=
Inscribed Worksheet
I. Identify each picture as showing a central angle, inscribed angle, interior angle, or exterior angle.
1. ______________
2.______________
3.______________
37
127
85
C
B
D
A
E
F
130
B
C
A
D
In Circle H, FE II GI and EI = 65
H
G
I
F
E
4. ______________
5.______________
6.______________
70
30
J
K
L
30
M
P
O
N
R
Q
S
T
III. Solve for the missing arc measure of angle measure.
7. m
76
U
V
W
Circle R
y
x
94
x
126
z
60
11.
»
_____
mNP
=
,
_____
mPMN
=
S
12.
»
mKL
= __________ 13. x = _______, y = _______
mYZ=85
X
Z
Y
25
mBD=90
B
D
C
38
K
L
J
64
H
G
I
15. x = _______
15.
»
mCD
= _______
16. m
112
A
R
N
M
C
A
Q
P
B
52
(5x - 6)
(2x+5)
I. Interior Angle Problems
The formula for interior angles is ________________________________.
67
161
p
c
b
113
Ex 1.
Ex 2.
243
y
37
C
B
A
Ex 3.
Ex 4.
II. Exterior Angle Problems
43
C
B
A
D
The formula for exterior angles is ________________________________.
120
10
D
Ex 5.
Ex 6.
E = 75
179
z
E
110x
Ex 7.
Ex 8.
Interior and Exterior Angles Worksheet
mF = 2
8
x
F
mG = 12
82
x
G
mF = 3
9
x
F
1. x = _______
2. x = ______
3. x = _______
mG = 47
179
x
G
130
20
J
mE = 21
96
x
E
4. x = _______
5. x = _______
6. x = _______
282
x
15
73
101
67
7. x = _______
8. x = _______
9. x = _______
133
23
203
23
121
203
10. x = _______
11. x = _______
12. x = _______
117
x
23
182
23
x
100
26
x
13. x = _______
14. z = ________
15.
_______
mD
=
R
54
202
x
78
Circle A with Diameter BC
38
x
A
B
C
86
98
x
16. x = _______
17. y = _______
18. x = _______
106
84
112
x
x
32
24
98
74
x
19. x = _______
20. x = _______
21. m
x
124
42
x
200
38
38
22. x = _______
23. x = _______
24. x = _______
x
86
62
112
Circle A with diameter BC
x
23
83
A
C
B
22. x = _______
23. x = _______
x
107
I.
x
107
Guided Mixed Problems – Central, Inscribed, Interior and Exterior Angles
x
78
1.
What type of angle?______ 2.
What type of angle?______
CB
is a________________.
GH
is a________________.
mB
R
=________
mK
R
=________
x
119
j
120
A
B
C
3.
What type of angle?______ 4.
What type of angle?______
DE
is a________________.
LN
is a________________.
»
mDF
=________
»
mTP
=________
II. For each circle, solve for the variable.
116
E
D
F
54
210
K
G
H
I
J
5. x = _____________
6. x = _____________
50
34
P
T
M
L
N
j
x
68
A
B
C
7. w = _____________
8. z = _____________
x
90
E
D
B
j
w
26
A
B
C
9. p = _____________
10. t = _____________
z
212
110
p
36
142
11. k = _____________
12. x = _____________
t
42
74
k
18
138
13. b = _____________
14. d = _____________
d
12
42
x
102
15. s = _____________
16. y = _____________
64
s
221
63
17. f = _____________
18. s = _____________
s
102
63
19. w = _____________
20. x = _____________
f
31
106
w
Complex pictures are formed by using multiple types of angles in one picture.
Start with a central angle. Add an inscribed angleAdd an exterior angle
Find
»
mAB
= ______
Find
mADB
S
= _____Find
»
mAD
= ____
y
116
Find
mACD
S
= _____Find
»
mFD
= ____
Find
mCAD
S
= _____Find
»
mFB
= ____
x
42
Find
mGEB
S
= ____
»
»
»
________
_______
______
______
mBC
mBOA
mAB
mDF
=
=
=
=
R
Example 1
1.
»
mEG
= _______
2.
mEHG
S
= ______
3.
»
mEK
= _______
4.
»
mML
= _______
Example 2
»
»
»
______
______
_____
______
mAGE
mAF
mAD
mCD
=
=
=
=
R
5.
mGFL
S
= ______
6.
»
mLG
= _______
7.
»
mEG
= _______
8.
mEHG
S
= ______
9.
»
mHL
= _______
10.
»
mML
= _______
11.
¼
mEM
= _______
12.
mEJK
S
= ______
Complex Pictures Worksheet
1. z = ________
2.
»
mCD
= _______
3. x =_____ y = _____
»
¼
_____
______
______
mEB
mECB
mA
=
=
=
R
»
»
______
______
______
mC
mED
mBC
=
=
=
R
95
48
t
4. x =_____ z=_____
5. a =_____ b=_____
6. t = ______
w =_____ y=_____
93
C
A
B
93
C
A
B
D
93
5
G
E
C
A
B
D
F
110
130
x
y
z
x
w
y
60
O
7.
8.
74
15
125
L
F
J
K
E
G
H
M
4
15
125
L
F
J
K
E
G
H
M
76
112
B
A
W
V
Z
X
Y
21
83
F
G
E
D
H
C
9.
»
____
mDC
=
»
____
mFG
=
10.
____
mXYZ
=
R
____
mVXY
=
R
____
mFDG
=
R
____
mDGC
=
R
____
mXVA
=
R
»
____
mXB
=
30
35
90
G
D
F
O
B
E
A
C
____
mCEG
=
R
»
____
mDF
=
____
mZ
=
R
º
____
mYB
=
64
24
76
z
y
x
E
A
B
D
C
Review
. Determining arc length and sector area
1. Find the length of
»
CA
2. Find the area of the shaded region
II. Use the circle and the following information to answer the questions below.
AD
and
FC
are diameters,
37
mFGA
=
o
S
,
GA
is an angle
bisector of
EGB
S
, and
»
32
mEF
=
o
11. Name a minor arc.
12. Name a major arc.
13. Find the measures of all central angles
14. Find the measures of all minor arcs
III. Solve the following problems.
15.
____
A
=
R
16. x = _______
17. x = ______
What type of angle?______ What type of angle?______ What type of angle?______
18. x = ______
19. x = _________
20. x = __________
21. x = _____
22. x = _____
23. x = _____
IV. Find the following values based on Circle A.
24. Find x ________
25. Find
»
BC
________
26. Find y ________
27. Find z ________
28. Find
»
DE
________
29. Find
»
EC
________
30. Find
»
CD
________
V. Equation of a circle
31. Given
22
(6)(7)49
xy
++-=
what is the center and the radius of the circle?
32. Given a circle centered at (3, 7) with a radius of 12 write the equation.
33. Write the equation for the following circle.
___________________________
142°
5 m
7 cm
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122°
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and radius 7
and radius 1
and radius 3
with radius 2
94°
b
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Circle E
Circle W
8 cm
136°
4 m
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8
62
A
x
159
47
16
x
x
167
105
x
294
x
106
9
47
x
52
54
x
30
x