Over Chapter 9
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Over Chapter 9
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Over Chapter 9
VWT
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Over Chapter 9
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Find the length of the image of MN under a dilation
with scale factor r = –3 and MN = 9.
27
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Over Chapter 9
Which of the following transformations does not
preserve length?
dilation
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• Identify and use parts of a circle.
• Solve problems involving the circumference
of a circle.
• circle
• center
• radius
• chord
• diameter
• congruent circles
• concentric circles
• circumference
• pi ()
The ratio of the circumference of a circle to its
diameter. The Greek letter  represents this
number. The value of pi is 3.1415926. . . .
Approximations for pi are 3.14 and 22/7.
• inscribed— every vertex of the lies on the circle.
• circumscribed—each side is tangent to the
circle.
Identify Segments in a Circle
A. Name the circle and identify a radius.
Identify Segments in a Circle
B. Identify a chord and a diameter of the circle.
A. Name the circle and identify a radius.
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B. Which segment is not a chord?
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B.
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B
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Find Radius and Diameter
If RT = 21 cm, what is the length of QV?
RT is a diameter and QV is a
radius.
d = 2r
21 = 2r
10.5 = r
Diameter Formula
d = 21
Simplify.
Answer: QV = 10.5 cm
If QS = 26 cm, what is the length of RV?
13 cm
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Find Measures in Intersecting Circles
Find Measures in Intersecting Circles
Since the diameter of
is 16 units, WY = 8.
Similarly, the diameter of
is 22 units, so XZ = 11.
WZ is part of radius XZ and part of radius WY.
First, find ZY.
WZ + ZY = WY
5 + ZY = 8
ZY = 3
Next, find XY.
XZ + ZY = XY
11 + 3 = XY
14 = XY
Find Measures in Intersecting Circles
Answer: XY = 14 units
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7 in.
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Find Circumference
CROP CIRCLES A series of crop circles was
discovered in Alberta, Canada, on September 4,
1999. The largest of the three circles had a radius of
30 feet. Find its circumference.
Since the radius is 30 feet, and d = 2r, the
diameter = 2(30) or 60 feet.
C = d
Circumference formula
= (60)
Substitution
= 60
Simplify.
≈ 188.50
Use a calculator.
Answer: The circumference of the crop circle is 60
feet or about 188.50 feet.
The Unisphere is a giant steel globe that sits in
Flushing Meadows-Corona Park in Queens,
New York. It has a diameter of 120 feet. Find its
circumference.
377.0 feet
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B
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Find Diameter and Radius
Find the diameter and the radius of a circle to the
nearest hundredth if the circumference of the circle
is 65.4 feet.
Circumference Formula
Substitution
Divide each side by .
Use a calculator.
Find Diameter and Radius
Radius Formula
Use a calculator.
Answer: d ≈ 20.82 ft; r ≈ 10.41 ft
Find the radius of a circle to the nearest hundredth
if its circumference is 16.8 meters.
2.67 m
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Read the Test Item
You need to find the diameter of the circle and use it to
calculate the circumference.
Solve the Test Item
The radius of the circle is the same length as either leg
of the triangle. The legs of the triangle have equal
length. Call the length x.
Pythagorean Theorem
Substitution
Simplify.
Divide each side by 2.
Take the square root
of each side.
So the radius of the circle is 3.
Circumference formula
Substitution
Answer: 6 units
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