7-4 Circles
Learn to identify parts of a circle and to
find central angle measures.
Course 2
7-4 Circles
Insert Lesson Title Here
Vocabulary
circle
center of a circle
radius
diameter
chord
arc
central angle
Sector
Pi Π
Course 2
7-4 Circles
A circle is the set of all points in a plane that are
the same distance from a given point, called the
center of a circle.
A circle is named by its center. For example, if
point A is the center of a circle, then the name
of the circle is circle A. There are special names
for the different parts of a circle.
Course 2
7-4 Circles
Arc
Part of a circle named
by its endpoints
Radius
Line segment
whose endpoints
are the center
of a circle and any
point on the circle
Course 2
Diameter
Line segment that
passes
through the center
of a circle, and
whose endpoints lie
on the circle
Chord
Line segment whose
endpoints are any two
points on a circle
7-4 Circles
Additional Example 1: Identifying Parts of a Circle
Name the parts of circle M.
A. radii
N
MN, MR, MQ, MO
B. diameters NR, QO
O
P
M
Q
C. chords
NR, QO, QN, NP
Reading Math
Radii is the plural form of radius.
Course 2
R
7-4 Circles
Try This: Example 1
Name the parts of circle M.
B
A
A. radii
C
GB, GA, GF, GD
G
B. diameters BF, AD
H
C. chords
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AH, AB, CE,
BF, AD
D
F
E
7-4 Circles
Sector
A central angle of a circle
is an angle formed by two
radii. A sector of a circle
is the part of the circle
enclosed by two radii and an
arc connecting them. (PIZZA)
The sum of the measures of all
of the central angles in a circle
is 360°. We say that there are
360° in a circle.
Course 2
)
Central angle
7-4 Circles
Additional Example 2: Problem Solving Application
The circle graph shows the results of a
survey about favorite types of muffins. Find
the central angle measure of the sector that
shows the percent of people whose favorite
type of muffin is blueberry.
Course 2
7-4 Circles
Additional Example 2 Continued
2
Make a Plan
There are 360° in a circle. Since the sector is
40% of the circle graph, the central angle is
40% of the 360° in the circle.
40% of 360° = 0.40 · 360°
3
Solve
0.40 · 360° = 144°
Multiply.
The central angle of the sector is 144°.
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7-4 Circles
Additional Example 2 Continued
4
Look Back
The 40% sector is less than half the graph, and
144° is less than half of 360°. Therefore, the
answer is reasonable.
Course 2
7-4 Circles
Circumference
C=Πd
or
C=2Πr
Π= 3.14
To find the Circumference,
multiply the diameter times Π (3.14)
or
Multiply the radius times 2 times Π (3.14)
Course 2
7-4 Circles
Circumference
C=Πd
or
C=2Πr
Find the circumference of the circle with
radius 3 mm.
C = 2 •Π•r
C = Π•d
C = 2 •Π•3
C = 3.14 • 6
C = 18.84 mm
C = 2 • 3.14 • 3
3 mm
C = 6 • 3.14
C = 18.84 mm
Course 2
7-4 Circles
Circumference
C=Πd
or
C=2Πr
Find the circumference of the circle with
diameter 4.5 cm.
C = Π•d
C = 3.14 • 4.5
C = 14.13 cm
4.5 cm
Course 2
7-4 Circles
Insert Lesson Title Here
Lesson Quiz
Name the parts of circle B.
1. radii
BA, BC
2. diameter(s) AC
3. chord(s)
DE, FE, AC
4. A pie is cut into 8 equal sectors. What is the
measure of the central angle of one slice of
pie? 45°
Course 2
7-4 Circles
Insert Lesson Title Here
Paper Plate Diagram
Your diagram must include all of the
following & each must be clearly
labeled:
• Center of a circle
• Radius
• Diameter
• Chord
• Arc
• Circumference
Course 2