Circle Vocabulary
C
Circle – set of all
points equidistant
_________
from a given point
called the _____
center
of the circle.
Symbol:
C
CHORD:
A segment
whose
endpoints
are on the
circle
DIAMETER:
P
Distance
across the
circle through
its center
Also known as the
longest chord.
RADIUS:
P
Distance
from the
center to
point on
circle
Formula
Radius = ½ diameter
or
Diameter = 2r
D = ?
r = ?
r = ?
D = ?
Use P to determine whether each
statement is true or false.
Q
1. RT is a diameter. False R
2. PS is a radius. True
P
3. QT is a chord. True
T
S
Secant Line:
intersects the
circle at
exactly TWO
points
Tangent Line:
a LINE that intersects the circle
exactly ONE time
Forms a 90°angle
with one radius
Point of Tangency:
The point where the
tangent intersects
the circle
Name the term that best describes the notation.
REVIEW
Identify the following parts of the circle.
D
C
1. DC • chord
2.
AB
•
radius
3.
AC
•
diameter
4.
line E •
5.
DC
•
A
B
E
tangent
secant
Note: The following are possible answers.
radius
diameter
chord
midpoint
secant tangent
Central Angles
An angle whose vertex is
at the center of the circle
Central angle
A
P
C
B
APB is a Central Angle
3 Types of Arcs
A
Major Arc
Minor Arc
More than 180°
Less than 180°
P
ACB
To name:
use 3 letters
C
AB
B
To name:
use 2 letters
Semicircle: An Arc that equals 180°
D
E
To name:
use 3 letters
P
F
EDF
Identify the parts
THINGS TO KNOW AND
REMEMBER ALWAYS
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are CONGRUENT
Linear Pairs are SUPPLEMENTARY
Formula
measure Arc = measure Central Angle
Measure of Arcs & Angles
In a circle, the measure of the central angle is
always equal to the measure of its intercepted arc.
x=n
m ∠ ABC = m AC
• If ∠ ABC is 80°, what
is the measure of arc
AC?
m AC = 80°
n°
C
A
x°
B°
Measure of Arcs & Angles
EXAMPLE: In the diagram below, if the m ∠ xyz is 68°, find
the measure of a.) minor arc and b.) major arc.
SOLUTION:
a. measure of minor arc
m ∠xyz = m xz (since ∠xyz is a central angle)
x
m xz = 68°
b. measure of major arc
68°
major arc = 360° – m xz (minor arc)
=360° – 68°
y
m xz (major arc) = 292°
292°
68°
z
Find the measures.
EB is a diameter.
m AB = 96°
A
E
m ACB= 264°
Q
m AE = 84°
96
B
C
Arc Addition Postulate
A
C
B
m ABC = m AB + m BC
Tell me the measure of the following arcs.
AC is a diameter.
m DAB =240
m BCA = 260
D
C
140
R
40
100
80
B
A
Congruent Arcs have the same measure and
MUST come from the same circle or of
congruent circles.
C
B
A
45
45
D
110
Arc length is proportional to “r”
Textbook
p. 396 #11
p. 404 #11 – 16, 25 – 30, 38