geometry chapter 9 study guide: circles 1.) 2.) 3.) 4.) 9 study guide answers.pdf · geometry...

Geometry Chapter 9 Study Guide: Circles

Necessary Skills: Pythagorean Theorem and Special Right Triangles. Solve for x and y 1.)

12

8x

2.)

y

x

460

30

3.)

x

y9

30

60

4.)

x

y

10

45

45

Key Vocabulary: Name one example of each 5.) a. radius c. chord e. tangent g. central angle i. minor arc

b. diameter d. secant f. point of tangency h. inscribed angle j. major arc

D

O

A

E

B

C

6.) Draw each: a. A rectangle inscribed in a circle Tangents:

b. A circle circumscribed about an obtuse triangle.

7.) Complete: JT is tangent to the circle at T a.) If OT = 4, JO = 12, then JT = ______ c.) If JK = 4 and KO = 6, then JT = ______

b.) If 30m J∠ = and JT= 12, JO = ____, OT = ____

K

O

J T

Central and Inscribed Angles: Solve for x and y 8.)

y

28

x

9.)

yx

65

10.)

70

y xOA B

C

11.)

y

x

50

12.)

110 yx

30

13.) 60

100y

xH

E

G

F

14.) y

x

62

60

15.)

60

100

xy

16.)

yx

40

Chords and Arcs: 17.)

x

120

D

A

B

C

18.) OT = 12, RS = 4, OR = ___, radius = ___, diameter=___

O

S

T

R

19.) CD = 6, OM = 4, ON = 3, EF = ___, radius = ___, diam. = ___

F

E

D

C

O

MN

20.) EF = 8, ON = 3, OM = 2, CD = _____

F

E

D

C

O

MN

Interior and Exterior Angles: Solve for x 21.)

x76

30

22.)

90

50

x

23.)

x

110

100

24.) x

90

170

25.)

40x

26.)

30 15x

Segments and Lengths: Solve for x 27.)

10

4 8

x

28.)

8 - xx

4

3

29.)

106

x

12

30.)

12

3

x

31.) 6

3x

x

32.)

93

5

x

Factor Completely 33.) x4 – 16

34.) x3 + x2 - 25x -25

Solve by Factoring 35.) x2 – 7x = 0

36.) 3x2 + 3x – 5 = x2 – 2x - 2