(9)­Circles.notebook
May 13, 2014
Intro to Circles
A circle is defined as the set of all points in a plane that are equidistant from a given fixed point called the center.
­A circle is named by its center. A cirlce with center C is called Circle C or C.
­Which of the following is a circle? Explain.
b
a
F
a
a=b
F
b
a≠b
1
(9)­Circles.notebook
May 13, 2014
Parts of the Circle:
Radius: segment from the center to edge
A
radius = 1/2 (diameter)
raduis
2(radius) = diameter
Diameter: chord that contains the center; Longest chord of the circle
radius = 1/2(diameter)
2(radius) = diameter
C
AB
A
.
diameter CB
B
B
D
Chord: segments whose endpoints
are on the circle
A
B
chord DB
Congruent Circles
: Circles are congruent if they have the same radius.
Interior of a Circle
: Set of all points inside a circle
Exterior of a Circle
: Set of all points outside a circle
2
(9)­Circles.notebook
May 13, 2014
Concentric Circles: Circles in the
same plane with the same center
but different radii
3
(9)­Circles.notebook
May 13, 2014
G
C
A
Practice:
E
B
D
H
F
a.) What is the name of this circle?
a.) What is the name of this circle?
b.) What is the radius?
b.) What is the radius?
c.) What is the diameter?
c.) What is the diameter?
d.) What is CG?
d.) What is EH?
e.) If AD is 2 units, and BF is 4 units, are these congruent circles?
Why or Why not?
4
(9)­Circles.notebook
May 13, 2014
Angles and Arcs
Central angle
:
­ Angle made of two radii.
­ Vertex of a central angle is the center
G
of the circle.
H
The Central Angle is
C or GCH
c
J
5
(9)­Circles.notebook
May 13, 2014
Arc­ an unbroken part of a circle
Minor Arc: arc smaller than half of the circle
(
Major Arc: arc larger than half of the circle
G
Minor Arc is GH
(
H
c
Major Arc is GJH
J
Why are 3 letters needed to name a Major Arc?
6
(9)­Circles.notebook
May 13, 2014
Practice
Use the figure below to answer the questions.
A
C
D
B
a.) Name the circle _______________
b.) Name the central angle in two ways ___________________
c.) Name the minor arc _____________
d.) Name the major arc _____________
7
(9)­Circles.notebook
May 13, 2014
­ an arc made by the diameter Semicircle
of a circle; the endpoints of the arc are the
endpoints of the diameter
o
­the measure is always 180
­name with 3 letters
R
X
(
(
XRY and XSY
are semicircles
Y
Q
S
8
(9)­Circles.notebook
May 13, 2014
The measure of an arc is defined to be the measu
of its central angle.
Minor Arc = central angle
Major Arc = 360 ­ central angle
B
A
( (
m AB = m ACB m AEB = 360 ­ ACB
62
C
E
9
(9)­Circles.notebook
Practice
Use the figure to the right to F
answer the questions.
May 13, 2014
G
150
E
a.) Name the circle _______________
H
b.) Name the central angle in two ways ___________________
c.) Name the minor arc _____________
d.) Name the major arc _____________
e.) Find the measure of the minor arc _____________
f.) Find the measure of the major arc _____________
10
(9)­Circles.notebook
May 13, 2014
: have exactly one point in common
Adjacent Arcs
(
(
.
Note: In C, PQ and QR are adjacent arcs.
P
110
Arc Addition Postulate
(
(
120
(
C
Q
m PQ + m QR = m PQR
R
11
(9)­Circles.notebook
May 13, 2014
Practice
Use the figure to the right to answer the questions.
J
L
M
120 75
K
a.) Name the circle _______________
b.) Name the adjacent arcs _________________
(
c.) Find the measure of JKL ________________
12
(9)­Circles.notebook
1.
May 13, 2014
2. Find mJKL.
13