4/14/2015
9-2 B Circles
circle-
the set of all points in a plane
that are the same distance from a given
point, called the center.
Center
radius
(plural: radii). A line segment
with one endpoint at the center of the circle
and the other endpoint on the circle.
Radius
Center
diameter - a chord that passes through the
center of the circle.
- the longest chords in a circle.
Radius
Center
Diameter
chord
- a line segment that has both
endpoints on the circle.
Radius
Center
Chord
Diameter
Example 1
Name the circle, a diameter, and three radii.
L
Z
M
N
The circle is circle Z.
LM is a diameter.
LN and LM are chords.
ZL, ZM, and ZN are radii.
The distance around a circle -circumference.
Circumference
Radius
Center
Diameter
The ratio of the circumference to the
diameter, C , is the same for any circle. This
d
ratio is represented by the Greek letter ,
which is read “pi.”
C
=
d
The decimal representation of pi starts with
3.14159265 . . . and goes on forever without
repeating. Most people estimate  using
either 3.14 or 22 .
7
The formula for the circumference of a circle is
C = d, or C = 2r.
Key Concept
Key Concept
Example 2
A skydiver is laying out a circular target for
his next jump. Estimate the circumference of
the target by rounding  to 3.
C = d
C3
•
Write the formula.
8
C  24 ft
Replace  with 3 and d
with 8.
Example 3
Find the missing value to the nearest
hundredth. Use 3.14 for pi.
d = 11 ft; C = ?
11 ft
C = d
C  3.14
Write the formula.
•
11
C  34.54 ft
Replace  with 3.14 and d with
11.
Example 4
Find each missing value to the nearest
hundredth. Use 3.14 for pi.
r = 5 cm; C = ?
5 cm
C = 2r
C2
•
3.14
C  31.4 cm
Write the formula.
•
5
Replace  with 3.14 and r
with 5.
Example 5
Find each missing value to the nearest
hundredth. Use 3.14 for pi.
C = 21.98 cm; d = ?
C = d
21.98  3.14d
21.98
3.14d
_______
 _______
3.14
3.14
7.00 cm  d
Write the formula.
Replace C with 21.98 and 
with 3.14.
Divide both sides by 3.14.
Example 6
The diameter of a circle is 48 centimeters.
Find the radius.
The radius is 24 centimeters.
Example 7
The radius of a circle is 9 inches.
Find the diameter.
d = 2r
d=2●9
d = 18
The diameter is 18 inches.
Example 8
John is making a table that has a top with a diameter of
24 inches. Find the circumference of the table. Round
to the nearest tenth.
C = d
C ≈ 3.14(24)
C ≈ 75.36
The distance around the table is about 75.36 inches.
Exit Ticket
Find the circumference of each circle. Use
3.14 for .
1.
8 in.
C = 25.12 in.
2.
3 in.
C = 18.84 in.
3. Find the circumference of a circle with a
diameter of 20 feet. Use 3.14 for .
62.8 ft
1. Identify the circumference of the given
circle. Use 3.14 for .
A. 31.14 in.
B. 31.21 in.
C. 31.33 in.
D. 31.4 in.
10 in.
2. Identify the circumference of the given
circle. Use 3.14 for .
A. 37.54 in.
B. 37.68 in.
C. 37.81 in.
D. 37.93 in.
6 in.
3. Identify the circumference of a circle with a
diameter of 26 feet. Use 3.14 for .
A. 81.64 ft
B. 81.73 ft
C. 81.86 ft
D. 81.92 ft
Homework
• Pg. 543 #1-28 Evens