10.1 circles and circumference 2017 ink.notebook
Page 90
March 13, 2018
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Page 92
Ch 10 Circles
10.1 Circles
and
Circumference
Lesson Objectives
Page 93
Standards
Lesson Notes
Page 94
10.1 Circles and Circumference
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10.1 circles and circumference 2017 ink.notebook
Standards
Lesson Objectives
Lesson Notes
After this lesson, you should be able to
successfully identify and use parts of
circles. You should also be able to find the
circumference of a circle.
March 13, 2018
Lesson Objectives
Standards
Lesson Notes
G.CO.1 Know precise definitions of angle, circle,
perpendicular line, parallel line, and line segment,
based on the undefined notions of point, line,
distance along a line, and distance around a
circular arc.
G.C.2 Identify and describe relationships among inscribed
angles, radii, and chords.
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Circle
Set of all points in a plane equidistant from a fixed point
Diameter
Any chord that
contains the center
of the circle
H
A circle consists of all points in a plane that are a given
distance, called the radius, from a given point called the center.
D
A segment or line can intersect a circle in several
ways.
J
Chord
A segment
whose
endpoints lie on
the circle
G
C
F
Radius
A Segment whose
endpoints are the
center of a circle
and a point on the
circle
E
K
L
Secant
A line that
contains a
chord
• A segment with endpoints that are at the center
and on the circle is a _____________.
• A segment with endpoints on the circle is a
_______________.
• A chord that passes through the circle's center
and made up of collinear radii is a _____________.
Tangent
A line in a plane
of a circle that
intersects the
circle in EXACTLY
one point
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10.1 circles and circumference 2017 ink.notebook
March 13, 2018
Radius
Diameter
d = 2r
r =1
2d
EXAMPLE
Name the circle:
A
B
E
F
Name all the:
Chords:
Radii:
D
C
Diameters:
The circumference of a circle is the distance
around the circle. For a circumference of C units
and a diameter of d units or a radius or r units,
C = 2¹ r
STOP!
C = d¹
Use 3.14 for
¹
1. Find the circumference of the circle to the nearest
hundredth.
13 cm
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10.1 circles and circumference 2017 ink.notebook
March 13, 2018
Finding the diameter and radius from the
circumference:
1)
2)
3)
4)
Divide circumference by 3.14
Your answer is the diameter
Divide the diameter by 2
Your answer is the radius
Find the diameter and radius of a circle with the given
circumference. Round to the nearest hundredth.
2. C = 40 in
When finding the exact circumference, do NOT type pi
or 3.14 into the calculator. Your answer will be in terms
of pi, for instance 5¹.
Find the exact circumference of each circle using the given inscribed or
circumscribed polygon.
3.
4.
5 cm
11 yd
12 cm
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10.1 circles and circumference 2017 ink.notebook
March 13, 2018
1. Name the circle.
2. Name radii of the circle.
O
A
3. Name chords of the circle
C
B
D
4. Name the circle.
A
X
5. Name radii of the circle.
6. Name chords of the circle.
7. Name diameters of the circle.
R
Y
B
8. If AB = 18 mm, find AR.
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10.1 circles and circumference 2017 ink.notebook
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9. If RY = 10 in, find AR and AB.
A
X
R
Y
B
Find the diameter and radius of a circle with the given
circumference. Round to the nearest hundredth.
11. C = 256 ft
12. C = 15.62 m
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10.1 circles and circumference 2017 ink.notebook
March 13, 2018
Find the exact circumference of each circle using the given
inscribed or circumscribed polygon.
Find the exact circumference of each circle using the given
inscribed or circumscribed polygon.
13.
15.
14.
8 cm
3 mm
7 mm
6 cm
9 in
16. WHEELS Zack is designing wheels for a concept car. The
diameter of the wheel is 18 inches. Zack wants to make
spokes in the wheel that run from the center of the wheel to
the rim. In other words, each spoke is a radius of the wheel.
How long are these spokes?
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10.1 circles and circumference 2017 ink.notebook
17. SEWING Ms. Singer is going to put lace around the edge of
the round tablecloth she just finished making. If the
tablecloth has a diameter of 12 ft. How much lace will she
need?
March 13, 2018
18. CAKE CUTTING Kathy slices through a circular cake. The
cake has a diameter of 14 inches. The slice that Kathy made
is straight and has a length of 11 inches.
Did Kathy cut along a radius, a diameter, or a chord of the circle?
On the
Worksheet
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10.1 circles and circumference 2017 ink.notebook
March 13, 2018
For Exercises 1­ 7, refer to ËP.
1. Name the circle.
2. Name a radius.
HOMEWORK
10.1 Practice WS on Circles and Circumference
A
D
C
3. Name a chord.
P
4. Name a diameter.
5. Name a radius not drawn
as part of a diameter.
E
B
6. Suppose the diameter of the circle is 16 cm.
Find the radius.
7. If PC = 11 in, find AB.
The diameters of ËF and ËG are 5 and 6 units, respectively.
Find each measure.
Find the diameter and radius of a circle with the given
circumference. Round to the nearest hundredth.
10. C = 36 m
11. C = 17.2 ft
12. C = 5 yd
8. BF
9. AB
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10.1 circles and circumference 2017 ink.notebook
March 13, 2018
Find the exact circumference of each circle using the given
inscribed or circumscribed polygon.
Find the exact circumference of each circle using the given
inscribed or circumscribed polygon.
13.
15.
14.
Find the exact circumference of each circle using the given
inscribed or circumscribed polygon.
17.
18.
16.
19. SUNDIALS Herman purchased a sundial to use as the
centerpiece for a garden. The diameter of the sundial is 9.5
inches.
a) Find the radius of the sundial.
b) Find the circumference of the sundial to the nearest
hundredth.
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10.1 circles and circumference 2017 ink.notebook
20. COINS Three identical circular coins are lined up in a row as
shown. The distance between the centers of the first and
third coins is 3.2 centimeters. What is the radius of one of
these coins?
22. EXERCISE HOOPS Taiga wants to make a circular loop that
he can twirl around his body for exercise. He will use a tube
that is 2.5 meters long.
March 13, 2018
21. PLAZAS A rectangular plaza has a surrounding circular
fence. The diagonals of the rectangle pass from one point on
the fence through the center of the circle to another point on
the fence. Based on the information in the figure, what is the
diameter of the fence? Round your answer to the nearest
tenth of a foot.
Answers:
a) What will be the diameter of Taiga's exercise hoop? Round
your answer to the nearest thousandth of a meter.
b) What will be the radius of Taiga's exercise hoop? Round your
answer to the nearest thousandth of a meter.
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