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Chapter 11 l Assignments 201

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Assignment Assignment for Lesson 11.1

Name _____________________________________________ Date ____________________

Riding a Ferris WheelIntroduction to Circles

Circle C is shown. Identify the indicated components of circle C.

1. Name the diameter(s).

C

B

FV

P

Q

R

2. Name the radius(radii).

3. Name the chord(s).

4. Name the tangent(s).

5. Name the secant(s).

6. Name the central angle(s).

7. Name the inscribed angle(s).

8. Name the major arc(s).

202 Chapter 11 l Assignments

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9. Name the minor arc(s).

10. Name the semicircle(s).

Draw the indicated part using each given circle.

11. Draw chord ST using circle C.

C

12. Draw tangent BC using circle S, where B is the point of tangency.

S

13. Draw secant LM using circle P.

P

14. Draw central angle XYZ using circle Y.

Y

15. Draw inscribed angle JKL using circle D.

D


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Name _____________________________________________ Date ____________________

Holding the WheelCentral Angles, Inscribed Angles, and Intercepted Arcs

Use circle S to answer each question. Explain your reasoning.

F

I

S

E

H

C

R

1. Suppose that m ⁀ CE � 59°. What is m ⁀ CFE ?

2. Suppose that m�CSI � 124°. What is m ⁀ FI ?

3. Suppose that m ⁀ CE � 55°. What is m�EFC?

4. Suppose that m�FSI � 71°. What is m ⁀ IC ?


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5. In circle E shown, m�ANG � 74°.

N

A

E

G

a. Determine m�AEG.

b. Determine m ⁀ ANG .

6. In circle H shown, m ⁀ CA � 105°, m ⁀ EA � 47°, and m ⁀ ET � 100°. T C

H

E A

a. Determine m�ETC.

b. Determine m�TCE.

c. Determine m�CAE.

d. Determine m�TEA.


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Name _____________________________________________ Date ____________________

Manhole Covers Measuring Angles Inside and Outside of Circles

1. In circle P shown, m ⁀ DE � 75° and m ⁀ NA � 49°. Determine m�DTE. D

N

AET

P

2. In circle K shown, m ⁀ DN � 144° and m�NCA � 68°. Determine m ⁀ EA .

D

EA

NK

C


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3. In circle O shown, m ⁀ SN � 55° and m ⁀ HA � 35°. Determine m�SCH. SN

AH

OC

4. In circle X shown, m ⁀ AS � 11° and m ⁀ MS � 104°. Determine m�DCM. A

S

D

M

XC


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Name _____________________________________________ Date ____________________

11

5. In circle S shown, m ⁀ ER � 38° and m ⁀ OT � 121°. Determine m�OUT.

UE

R

O

T

S

6. In circle M shown, ___

XE is a diameter of the circle and m ⁀ XT � 132°.

U

E

M

X

T P

Draw a chord that connects points X and T. Then determine m�XUT.


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7. In circle G shown, OH � ES, m ⁀ OH � 41°, and U

O

S

E

H

G

41°

41°

171°

m ⁀ HE � 171°. Determine m�EUH.

8. In circle B shown, m ⁀ HE � 99°. Determine m�HUE.

R

H

BU

E

9. In circle T shown, m�RCE � 57° and m ⁀ RE � 141°.

CL

B

R

T

E

Determine m ⁀ BL .


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Name _____________________________________________ Date ____________________

Color Theory Chords

1. Use circle T to complete parts (a) through (g).

T

a. Draw an inscribed right angle in circle T. Label each point where the angle

intersects the circle. What is the name of the right angle?

b. Draw the chord determined by the inscribed right angle. What is the name of

the chord?

c. What else do you know about the chord determined by an inscribed right angle?

d. Draw a second inscribed right angle in circle T. Label each point where the

angle intersects the circle. What is the name of the second right angle?

e. Draw the chord determined by the second inscribed right angle. What is the

name of the chord?

f. What else do you know about the chord determined by the second inscribed

right angle?


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g. Do you think every inscribed right angle will determine the longest chord of the

circle, which is the diameter of the circle? Explain your reasoning.

2. The figure shows a section of a circle. Draw two chords and construct their

perpendicular bisectors to locate the center of the circle.

3. In circle G shown below, MG � 1.84 centimeters, GL � 1.98 centimeters,

m�GLH � 90°, and m�GMK � 90°. Determine which chord is longer,

IH or JK. Explain your reasoning.

G

I

L

H

J

M

K


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Name _____________________________________________ Date ____________________

Solar Eclipses Tangents and Secants

1. Use circle O to complete parts (a) through (h).

O

a. Draw a tangent to circle O. Label the point of tangency as point A.

b. Label another point on the tangent you drew in part (a) as point B.

c. Draw a second tangent line to circle O that passes through point B. Label this

second point of tangency as point C.

d. Draw the radii ___

OA and ____

OC .

e. What is m�OAB? Explain your reasoning.

f. What is m�OCB? Explain your reasoning.


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g. Use a protractor to determine the measure of �AOC.

h. What is m�ABC? Explain your reasoning.

2. In the figure shown, rays LJ and LH are tangent to circle K,

KJ

H

L

and the measure of angle LJH is 71°. What is the measure

of angle JLH? Explain your reasoning.

3. In the figure shown, WV � 36 inches, point X is a midpoint

T

Y

XW

Z

Vof segment WV, and YV � 40 inches. What is YZ? Explain

your reasoning.


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Name _____________________________________________ Date ____________________

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4. In the figure shown, line FG is tangent to circle Q, BC � 10 feet, and

Q

F

B

C

G

CG � 4 feet. What is FG? Explain your reasoning.


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Name _____________________________________________ Date ____________________

Replacement for a Carpenter’s Square Inscribed and Circumscribed Triangles and Quadrilaterals

1. In the figure shown, � ABC is inscribed in circle D and m� A � 55°.

D

A

B

C

What is m�C? Explain your reasoning.

2. In the figure shown, � XYZ is inscribed in circle W and XY � YZ.

W

Z

X

Y

What is m�X? Explain your reasoning.

3. In the figure shown, � RST is inscribed in circle Q, RS � 18 centimeters,

Q

S

T

Rand ST � 24 centimeters. What is RT? Explain your reasoning.


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4. In the figure shown, quadrilateral FGHJ is inscribed in circle K,

K

J

F

G

H

m�F � 112°, and m�G � 87°. What are m�H and m�J?

Explain your reasoning.

5. In the figure shown, quadrilateral LMNP is inscribed in circle R,

R

P

LM

N

m�P � 57°, and m� L � m�N. What are m�M, m� L, and m�N?

Explain your reasoning.


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Name _____________________________________________ Date ____________________

GearsArc Length

1. In circle A shown describe the difference between the measure of

A

B

C

minor arc BC and the length of minor arc BC. Use complete

sentences in your answer.

2. In circle E shown, the radius of the circle is 16 centimeters and

E

S

B

J

m�JSB is 40°. Determine the arc length of ⁀ JB . Use complete sentences

in your answer.


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3. In circle I shown, the radius is 6 millimeters and m ⁀ HC is 80°. S

R

IC

H

D80°

Determine the arc length of ⁀ SC . Use complete sentences

in your answer.

4. In circle H shown, the arc length of ⁀ SJ is 24� centimeters

S

O

J

Hand m�JOS is 80°. Determine the length of a diameter of

circle H. Use complete sentences in your answer.


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Name _____________________________________________ Date ____________________

Playing DartsSectors and Segments of a Circle

In circle C shown, � ABC is an equilateral triangle and AC � 10 inches.

AB

C

10 in.

1. Calculate the area of sector ACB. Express your answer in terms of � and as

a decimal rounded to the nearest hundredth.

2. The height of � ABC is approximately 8.66 inches. Calculate the area of � ABC.

3. Calculate the area of segment AB of circle C. Express your answer in terms of

� and as a decimal rounded to the nearest hundredth.


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In circle A shown, the radius is 18 centimeters and � ABC is an equilateral triangle.

A

B

C

18 cm

4. Calculate the area of the sector of circle A that is bounded by radii AB and AC.

Express your answer in terms of � and as a decimal rounded to the nearest

hundredth.

5. Calculate the area of the segment of circle A that is bounded by chord BC. Express

your answer in terms of � and as a decimal rounded to the nearest hundredth.


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In circle S shown, the radius is 22 feet and m�RST � 90°.

22 ftR

S

T

6. Calculate the area of the sector of circle S that is bounded by radii SR and ST.

Express your answer in terms of � and as a decimal rounded to the

nearest hundredth.

7. Calculate the area of the segment of circle S that is bounded by chord RT. Express

your answer in terms of � and as a decimal rounded to the nearest hundredth.


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Name _____________________________________________ Date ____________________

The Coordinate Plane Circles and Polygons on the Coordinate Plane

1. In circle C shown, chords AB and DE intersect at point F. Show that the product of

the lengths of the segments of chord AB is equal to the product of the lengths of

the segments of chord DE. Then determine the theorem that is illustrated. Show all

your work.

y

–2

–4

–6

–8

2

4

6

8

20 4 6 8–8 –6 –4 –2 x

D (–8, 6)

B (0, 10)

F (–5, 5)

E (10, 0)C (0, 0)

A (–10, 0)


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2. Triangle JKL is inscribed in circle D. Show that � JKL is an isosceles right triangle.

Show all your work.

y

–2

–4

–6

–8

2

4

6

8

20 4 6 8–8 –6 –4 –2 x

K (–4, 3)

L (4, –3)

D (0, 0)

J (–3, –4)


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Name _____________________________________________ Date ____________________

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3. Quadrilateral WXYZ is a kite. Draw the quadrilateral formed by connecting the

midpoints of the sides of the kite and label this quadrilateral ABCD. Then classify

quadrilateral ABCD. Show all your work.

y

–2

–4

–6

–8

2

4

6

8

20 4 6 8–8 –6 –4 –2 x

Y (8, 6)

X (0, 8)

Z (0, –8)

W (–8, 6)

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