3 APPLY
ASSIGNMENT GUIDE
BASIC
Day 1: pp. 632–634 Exs. 10–30
even
Day 2: pp. 632–635 Exs. 11–31
odd, 33–35, 40–54 even,
Quiz 2 Exs. 1–7
GUIDED PRACTICE
Vocabulary Check
✓
Concept Check
✓
Skill Check
✓
1. Sketch a circle with a secant segment. Label each endpoint and point of
intersection. Then name the external segment. Check students’ drawings.
segments in the figure at the
right related to each other? GH • HK = FH • HJ
Day 1: pp. 632–634 Exs. 10–30
even
Day 2: pp. 632–635 Exs. 11–31
odd, 33–35, 40–54 even,
Quiz 2 Exs. 1–7
H
F
K
Fill in the blanks. Then find the value of x.
? = 10 • 㛭㛭㛭
?
3. x • 㛭㛭㛭
15; 18; 12
AVERAGE
J
G
2. How are the lengths of the
? • x = 㛭㛭㛭
? • 40
4. 㛭㛭㛭
12; 15; 50
x
18
? = 8 • 㛭㛭㛭
?
5. 6 • 㛭㛭㛭
16; x + 8; 4
x
10
15
10
6
12
15
25
8
x
ADVANCED
Day 1: pp. 632–634 Exs. 10–32
even
Day 2: pp. 632–635 Exs. 11–31
odd, 33–39, 40–54 even,
Quiz 2 Exs. 1–7
? + x)
6. 42 = 2 • ( 㛭㛭㛭
2; 6
3
4
APPLICATION NOTE
EXERCISE 9 The figure with the
most area for a given perimeter is a
circle. Cylindrical cages provide the
most volume (habitat space) for a
given height because the base is a
circle.
632
5
4
x
x
pp. 632–634 Exs. 10–30 even
(with 10.4)
pp. 632–635 Exs. 11–31 odd,
33–35, 40–54 even, Quiz 2
Exs. 1–7 (with 10.6)
HOMEWORK CHECK
To quickly check student understanding of key concepts, go
over the following exercises:
Exs. 10, 14, 16, 18, 22, 26, 30. See
also the Daily Homework Quiz:
• Blackline Master (Chapter 10
Resource Book, p. 81)
•
Transparency (p. 76)
? = 㛭㛭㛭
?
8. x • 㛭㛭㛭
x + 3; 22; 1
x
BLOCK SCHEDULE
EXERCISE LEVELS
Level A: Easier
10–12
Level B: More Difficult
13–35
Level C: Most Difficult
36–39
?
7. x 2 = 4 • 㛭㛭㛭
9; 6
2
9.
2
ZOO HABITAT A zoo has a large circular aviary, a habitat for birds.
You are standing about 40 feet from the aviary. The distance from you to
a point of tangency on the aviary is about 60 feet. Describe how to estimate
the radius of the aviary. The segment from you to the center of the aviary is a secant
segment that shares an endpoint with the segment that is tangent to the aviary. Let x be
the length of the internal secant segment (twice the radius of the aviary) and
50
2
PRACTICE AND APPLICATIONS use Thm. 10.17. Since 40(40 + x) ≈ 60 , the radius is about }2} = 25 ft.
STUDENT HELP
FINDING SEGMENT LENGTHS Fill in the blanks. Then find the value of x.
Extra Practice
to help you master
skills is on p. 822.
? = 12 • 㛭㛭㛭
?
10. x • 㛭㛭㛭
9; 15; 20
? = 㛭㛭㛭
? • 50
11. x • 㛭㛭㛭
45; 27; 30
x
45
x
12
9
HOMEWORK HELP
Example 1: Exs. 10,
14–17, 26–29
Example 2: Exs. 11, 13,
18, 19, 24, 25
632
x
12
15
7
50
FINDING SEGMENT LENGTHS Find the value of x.
13
28
13.
14.
Chapter 10 Circles
9
27
15
STUDENT HELP
?
12. x2 = 9 • 㛭㛭㛭
16; 12
x
4
x
7
8.5
17
16
23
15.
x
24
12
STUDENT HELP
FINDING SEGMENT LENGTHS Find the value of x.
HOMEWORK HELP
16.
17.
2
Example 3: Exs. 12,
20–23, 25–27
Example 4: Exs. 12,
20–23, 25–27
x
x
9 2x
10
40
xⴙ1
x
78
2
3
8 }}
19.
24
20.
x
21.
12
12
4
x
18
4
43 }}
72
8
15
1
3
18.
6
INT
NE
ER T
36
x
22.
8
12
23.
HOMEWORK HELP
Visit our Web site
www.mcdougallittell.com
for help with using the
Quadratic Formula in
Exs. 21–27.
10
24.
11
29
x
15
x
x
35
9
º9 + 兹56
苶5苶
}} ≈ 7.38
2
–29 + 兹38
苶41
苶
}} ≈ 16.49
2
xy USING ALGEBRA Find the values of x and y.
25.
8
30
x
28.
20
26.
8
12
27.
2
x
3
x
y
STUDENT HELP NOTES
Homework Help Students can
find help for Exs. 21–27 at
www.mcdougallittell.com.
The information can be printed
out for students who don’t have
access to the Internet.
8
6
STUDENT HELP
COMMON ERROR
EXERCISE 19 Watch for students
who find x = 12 because they calculate using the equation 4 ⫻ 18 =
6 ⫻ x instead of the equation
4(18 + 4) = 6(6 + x).
TEACHING TIPS
EXERCISE 29 Remind students
that a diameter that is perpendicular to a chord bisects the chord.
Since the stairs are built symmetrically, the diameter is perpendicular
to the chord.
y
6
14
8
18
º13 + 5兹17
苶
x = 12, y = 2兹13
苶 ≈ 7.21 x = 7, y = }
x = 42, y = 10
} ≈ 3.81
2
DESIGNING A LOGO Suppose you are
designing an animated logo for a television
commercial. You want sparkles to leave
point C and move to the circle along the
segments shown. You want each of the
sparkles to reach the circle at the same time.
To calculate the speed for each sparkle, you
need to know the distance from point C to
the circle along each segment. What is the
distance from C to N? 18
29. 4.875 ft; the diameter
29.
BUILDING STAIRS You are
through A bisects the
making curved stairs for students
chord into two 4.5 ft
to stand on for photographs at a
segments. Use Thm. 10.15
homecoming dance. The diagram
to find the length of the
shows a top view of the stairs.
part of the diameter
What is the radius of the circle
containing A. Add this
length to 3 and divide by 2
shown? Explain how you can use
to get the radius.
Theorem 10.15 to find the answer.
10
15
C
12
N
9 ft
3 ft
10.5 Segment Lengths in Circles
633
633
30.
FOCUS ON
APPLICATIONS
APPLICATION NOTE
EXERCISE 30 The GPS provides
signals that can be used to
compute velocity and time as
well as position. Additional
information about the Global
Positioning System is available
at www.mcdougallittell.com.
EC
EA
Prop., (EA) 2 = EC ⴢ ED.
L
AL I
GPS Some cars
have navigation
systems that use GPS to tell
you where you are and how
to get where you want to go.
RE
INT
31.
APPLICATION LINK
Æ
EB
35. The distances over which
most inhabitants of Earth
are able to see are
relatively short and the
curvature of Earth over
such distances is so small
as to be unnoticeable.
39. Sample answer: If tangent
segments to 2 intersecting
›s share a common
endpoint outside the 2 ›s,
For more Mixed Review:
•
Search the Test and Practice
Generator for key words or
specific lessons.
634
Not drawn
to scale
B
A
Æ
C
D
that ¤BCE and ¤DAE are similar. Use the
31. Draw AD
xxx and BC
xxx. Then
inscribed angles ™EBC
fact that corresponding sides of similar
and ™EDA intercept the
triangles are proportional.
same arc, so ™EBC £
PROVING THEOREM 10.17 Use the plan to write a paragraph proof.
™EDA. ™E £ ™E by the 32.
Reflexive Prop. of Cong.,
See margin.
Æ
Æ
GIVEN 䉴 EA is a tangent segment and ED
A
so ¤BCE ~ ¤DAE by the
is a secant segment.
AA Similarity Post. Then
since lengths of corresp.
PROVE 䉴 (EA)2 = EC • ED
E
sides of ~◊ are
C
Æ
Æ
EA
ED
D
Plan for Proof Draw AD and AC. Use
proportional, }} = }}. By
Test
Preparation
• Practice Levels A, B, and C
(Chapter 10 Resource Book,
p. 70)
• Reteaching with Practice
(Chapter 10 Resource Book,
p. 73)
•
See Lesson 10.5 of the
Personal Student Tutor
C
E
Plan for Proof Draw AD and BC, and show
www.mcdougallittell.com
EC
For Lesson 10.5:
12,500 mi
PROVING THEOREM 10.16 Use the plan to write a paragraph proof.
See margin.
Æ
Æ
GIVEN 䉴 EB and ED are secant segments.
PROVE 䉴 EA • EB = EC • ED
NE
ER T
the fact that corresponding sides of similar
triangles are proportional.
Cross Product Prop.,
EA • EB = EC • ED.
ADDITIONAL PRACTICE
AND RETEACHING
B
៣
FE
32. Draw A
苶D
苶 and A
苶C苶. åADE is an
inscribed å, so
1 ä
. åCAE is formed
måADE = }}mAC
2
by a tangent and a chord, so
1 ä
. Then åADE •
måCAE = }}mAC
2
åCAE. Since åE • åE by the
Reflexive Prop. of Cong., †ACE Í
†DAE by the AA Similarity Post.
Then since lengths of corresp.
sides of Í †s are proportional,
EA ED
}} = }}. By the Cross Product
GLOBAL POSITIONING SYSTEM
Satellites in the Global Positioning System
D
(GPS) orbit 12,500 miles above Earth. GPS
A
signals can’t travel through Earth, so a
satellite at point B can transmit signals only
to points on AC . How far must the satellite
Earth
be able to transmit to reach points A and C?
Find BA and BC. The diameter of Earth is
F
about 8000 miles. Give your answer to the
nearest thousand miles. about 2500兹41
苶 ≈ 16,008 mi
MULTI-STEP PROBLEM In Exercises 33–35, use the
following information.
A person is standing at point A on a beach and looking
2 miles down the beach to point B, as shown at the right.
The beach is very flat but, because of Earth’s curvature,
Æ
the ground between A and B is x mi higher than AB.
x mi
A
B
1 mi
8000 mi
33. Find the value of x. about 0.000125 mi
34. Convert your answer to inches. Round to the
nearest inch. 8 in.
35.
Writing
Not drawn to scale
Why do you think people historically thought that Earth was flat?
See margin.
Æ˘
Æ˘
A
Challenge In the diagram at the right, AB and AE are
the tangent segments are tangents.
E
£. The conjecture is not
true in general. Let A be 36. Write an equation that shows how AB is related
C
the common endpoint and
to AC and AD. (AB)2 = AC • AD
B
C and D the points of
D
intersection as shown in 37. Write an equation that shows how AE is related
the figure. The conjecture
to AC and AD. (AE)2 = AC • AD
is true if and only if A, C,
2
2
38. How is AB related to AE? Explain. AB = AE; (AB) = (AE) and AB
and D are collinear.
and AE are both positive.
EXTRA CHALLENGE
39. Make a conjecture about tangents to intersecting circles. Then test your
www.mcdougallittell.com
conjecture by looking for a counterexample. See margin.
★
634
Chapter 10 Circles
MIXED REVIEW
4 ASSESS
FINDING DISTANCE AND MIDPOINT Find AB to the nearest hundredth.
DAILY HOMEWORK QUIZ
Æ
Then find the coordinates of the midpoint of AB . (Review 1.3, 1.5 for 10.6)
冉
1
冊
40. A(2, 5), B(º3, 3) 5.39; º}2}, 4
7 3
42. A(º8, º6), B(1, 9) 17.49, º}}, }}
41. A(6, º4), B(0, 4) 10; (3, 0)
44. A(0, º11), B(8, 2)
45. A(5, º2), B(º9, º2) 14, (º2, º2)
冉 2 2冊
9
15.26, 冉4, º}}冊
2
冉
Transparency Available
Find the values of x and y.
1.
6
冊
11
43. A(º1, º5), B(º10, 7) 15; º}2}, 1
46. y = º2x º 5, (º2, º1)
1
2
y = }}x
x
2
3
47. y = ᎏᎏ x + 4, (6, 8) y = º}}x + 17
2
3
48. y = ºx + 9, (0, 9) y = x + 9
1
50. y = ᎏᎏ x + 1, (º10, º1)
5
y = º5x º 51
7
51. y = ºᎏᎏ x º 5, (º6, 9) y = }3}x + }81}
3
7
7
DRAWING TRANSLATIONS Quadrilateral ABCD has vertices A(º6, 8),
B (º1, 4), C (º2, 2), and D(º7, 3). Draw its image after the translation.
(Review 7.4 for 10.6) 52–54. See margin.
冉
11
53. (x, y) ˘ (x º 2, y + 3) 54. (x, y) ˘ x, y º ᎏᎏ
2
QUIZ 2
冊
Find the value of x. (Lesson 10.4)
2. 139
xⴗ
158ⴗ
110ⴗ
3. 26
xⴗ
xⴗ
8
10
x
4.5
EXTRA CHALLENGE NOTE
Self-Test for Lessons 10.4 and 10.5
1. 202
8.4
2.
1
10
49. y = 3x º 10, (2, º4) y = º}}x º }}
3
3
52. (x, y) ˘ (x + 7, y)
x⫹1
5
WRITING EQUATIONS Write an equation of a line perpendicular to the
given line at the given point. (Review 3.7 for 10.6)
82ⴗ
Challenge problems for
Lesson 10.5 are available in
blackline format in the Chapter 10
Resource Book, p. 77 and at
www.mcdougallittell.com.
ADDITIONAL TEST
PREPARATION
1. WRITING Describe how to
find the length of the tangent
segment in the figure below.
Solve (AB) 2 = BC ⴢ BD to find AB.
28ⴗ
A
B
168ⴗ
C
Find the value of x. (Lesson 10.5)
4.
1
6 }}
4
5.
6
x
5
20
16
8
10
x
6.
5
D
10
18
x
7. Solve 20(2r + 20) = 49 2
(Thm. 10.17) or solve
(r + 20)2 = r 2 + 49 2 (the
Pythagorean Theorem );
50.025 ft.
7.
SWIMMING POOL You are standing
20 feet from the circular wall of an above
ground swimming pool and 49 feet from
a point of tangency. Describe two different
methods you could use to find the radius
of the pool. What is the radius? (Lesson 10.5)
T
20 ft
r
ADDITIONAL RESOURCES
An alternative Quiz for Lessons
10.4–10.5 is available in the
Chapter 10 Resource Book, p. 78.
15
52–54. See Additional Answers
beginning on page AA1.
49 ft
r
P
r
10.5 Segment Lengths in Circles
635
635