Name: Period GL

UUNITNIT 16: C 16: CIRLCESIRLCES

I can define, identify and illustrate the following terms: Interior of a circleExterior of a circleChord Secant of a circleTangent to a circle

Point of tangencyArcMajor ArcMinor ArcArc LengthInscribed Angle

Central angle of a circleSemicircleSector of a circleSegment in a circleConcentric CirclesCircumscribed

Dates, assignments, and quizzes subject to change without advance notice.Monday Tuesday Block Day Friday

11/12Introduction to Circles

Computer Lab

13Inscribed Angles

16Interior and Exterior

Angles

17Mixed Angles

18/19Quiz

Complex Angles

20Review

23TEST: Circles

Block Day, 5/11-12/11Introduction 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, 5/13/11Inscribed Angles

I can find the measure of an angle associated with a circle Apply the properties of arcs

PRACTICE: Inscribed Angles Worksheet

Monday, 5/16/11Interior 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, 5/17/11Mixed Angles

I can find the measure of an angle associated with a circle Apply the properties of arcs

PRACTICE: Mixed Angles Worksheet

Block Day, 5/18-19/11Complex Angles

I can find the measure of an angle associated with a circle Apply the properties of arcs

PRACTICE: Complex Angles WorksheetQUIZ: Circles

Friday, 5/20/11REVIEW

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

Block5/11-12

Find the length of . Find the area of the shaded region

Friday5/13

Given what is the center and the radius of the circle?

and are diameters, , is an angle bisector of , and . Find all the central angle measurements.

Monday5/16

Find x. Find x.

Tuesday5/17

Find x. Find m<A.

CB

A

142° 5 m

7 cm

GF C

B

E

A

D

GF C

B

E

A

D

28

x

x

300

x 170122

6

54

A

Block5/18-19

Given a circle centered at (2, 9) with a radius of 9 write the equation.

Find x

Friday5/20

a =_____ b=_____ Find x

x112 6

b165

106

a 20

x

Equation of a Circle Notes

where (h, k) is the _____________ and r is the __________

EXAMPLE:

1. What is the center and radius of the following circle? 2. Write the equation for the following circle.

Center = ____________

Radius = ___________

3. Given a radius of (-2, 12) and a radius of 11 write the equation of the circle.

Central Angle NotesThe 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.

Ex 1:

Ex 2:

Ex 3:

Ex 4:

Ex 5:

Ex 6:

Ex 7:

37

127

85

CB D

A

E

F

122°

Introduction to Circles WorksheetI. Use the picture at the right to answer the following questions.

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 ________

80

126

E

B

F

O

A

C

D

5

90 A

C

G

F

D

E

B

II. Use the picture below for questions 1-10. is a diameter and 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.

III. Use the picture below to answer questions 11 -20. and are diameters of the circle.

11. 16.

12. 17.

13. 18.

14. 19.

15. 20.

III. Find the center and radius from each equation.

21. 22.

23. 24.

IV.

40

100

K

A

C

B

E

D

and radius 7

and radius 1

and radius 3with radius 2

7. 8.

9. 10.

38

K

L

J

64

H

G

I

112

A

R

N

M

C

A

Q

P

B

The relationship between an inscribed angle and its intercepted arc can be written two ways:

Angle measure = ______________ OR Arc measure = _______________ EXAMPLES: 1: =_________ 2: =_________

3: =_________ 4: =_________

5. =_________ 6. ,

Inscribed WorksheetI. Identify each picture as showing a central angle, inscribed angle, interior angle, or exterior angle.

37

C

B

A

43

C

B

A D

1. ______________ 2.______________ 3.______________

4. ______________ 5.______________ 6.______________

III. Solve for the missing arc measure of angle measure.

7. m<CAD = ______ 8. <X = __________ 9. m<V= __________ 10. m<T = _______

11. , 12. = __________ 13. x = _______, y = _______

15. x = _______ 15. = _______ 16. m<FIG = _________ 18. z = ___________

130

B CA

D

In Ci rcle H, FE II GI and EI = 65

H

G

I

F

E

70

30

J

K

L30

M

PO

N

RQ S

T

76

U

V

W

Circle R

y

x

94

x126

z

60

mYZ=85

X

ZY

25

mBD=90

B D

C

52

(5x - 6)

(2x+5)

67

161

p

c

b

113 76

U

V

W

x126

243

y

I. Interior Angle Problems

The formula for interior angles is ________________________________.

Ex 1. Ex 2.

Ex 3. Ex 4.

II. Exterior Angle Problems

The formula for exterior angles is ________________________________.

Ex 5. Ex 6.

Ex 7. Ex 8.

1573

10167

133

23

203

23

121

203

78

Circle A with Diameter BC38

xA

B

C

x

107x

107

Interior and Exterior Angles Worksheet

1. x = _______ 2. x = ______ 3. x = _______

4. x = _______ 5. x = _______ 6. x = _______

7. x = _______ 8. x = _______ 9. x = _______

10. x = _______ 11. x = _______ 12. x = _______

13. x = _______ 14. z = ________ 15.

120

10D

E = 75

179z

E

mF = 2

8

x

F

23

182

23x100

26

x

54

202

x

78

Circle A with Diameter BC38

xA

B

C

86

98

x106 84

112

x

x

32

24 98

74

x x

124

42

x200

38

38

x86

62

112

Circle A with diameter BC

x

23

83

A

C

B

16. x = _______ 17. y = _______ 18. x = _______

19. x = _______ 20. x = _______ 21. m<J = _______

22. x = _______ 23. x = _______ 24. x = _______

22. x = _______ 23. x = _______

110x

mG = 12

82

x

G

243

y

mF = 3

9

x

FmG = 47

179

x

G

130

20

J

mE = 21

96

x

E

282

x

117x 94°

x

78

x

119

I. Guided Mixed Problems – Central, Inscribed, Interior and Exterior Angles

1. What type of angle?______ 2. What type of angle?______

is a________________. is a________________.

=________ =________

3. What type of angle?______ 4. What type of angle?______

is a________________. is a________________.

=________ =________

II. For each circle, solve for the variable.

5. x = _____________ 6. x = _____________

7. w = _____________ 8. z = _____________

9. p = _____________ 10. t = _____________

j120

A

B

C

116

E

D

F

54

210

K

G

H

I

J

5034 P

T

M

LN

j

x

68

A

B

C

x90E

D

B

j

w

26A B

C

z

212

110

p36

142

t

4274

11. k = _____________ 12. x = _____________

13. b = _____________ 14. d = _____________

15. s = _____________ 16. y = _____________

17. f = _____________ 18. s = _____________

19. w = _____________ 20. x = _____________

k

18

138

d

12

42

x

102

64

b

s

221

63

s

102

63

f

31

106

w

y116

x

42

Complex pictures are formed by using multiple types of angles in one picture.

Start with a central angle. Add an inscribed angle Add an exterior angle

Find = ______ Find = _____ Find = ____

Find = _____ Find = ____

Find = _____ Find = ____

Find = ____

Example 11. = _______

2. = ______

3. = _______

4. = _______

Example 2

5. = ______

6. = _______

7. = _______

8. = ______

9. = _______

10. = _______

11. = _______

12. = ______

93

C

AB

93

C

AB

D

93

5

G

E

C

AB

D

F

74

15

125

L

F

J

K

EG

HM

4

15

125

LF

J

KEG

H

M

76

112

B

A

W

V

Z

X

Y

21

83 F

G

E

D

HC

Complex Pictures Worksheet

1. z = ________ 2. = _______ 3. x =_____ y = _____

4. x =_____ z=_____ 5. a =_____ b=_____ 6. t = ______

w =_____ y=_____

7. 8.

9. 10.

80

126

E

B

F

O

A

C

D

z

60 25

mBD=90

B D

C

95

48

tb

165

106

a

110

130

x

y

z

xw

y60

O

Circle ECircle W

30

35

90

G

D

FO

B

EA

C

Review. Determining arc length and sector area

1. Find the length of 2. Find the area of the shaded region

II. Use the circle and the following information to answer the questions below.and are diameters, , is an angle

bisector of , and

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. 16. x = _______ 17. x = ______ What type of angle?______ What type of angle?______ What type of angle?

______

18. x = ______ 19. x = _________ 20. x = __________

GF C

B

E

A

D

CB

A

136° 4 m

8 cm

8

62

A

16

x

x

159

47

x106 9

x

294

x 167105

21. x = _____ 22. x = _____ 23. x = _____

IV. Find the following values based on Circle A.

24. Find x ________

25. Find ________

26. Find y ________

27. Find z ________

28. Find ________

29. Find ________

30. Find ________

V. Equation of a circle

31. Given 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.

___________________________

64

24

76

z

y

x

E

A

B

D

C

30

x

52

54 x

47

x