Lesson 6.2
Find Arc Measures
Pg 191
Central angle
• Central angle- angle whose vertex is the
center of a circle
A
ACB is
a central
angle
C
B
Arcs
A
• Arc- a piece of a circle.
Named with 2 or 3 letters
Measured in degrees
B
• Minor arc- part of a circle that measures
less than 180o (named by 2 letters).
P
(
B
BP
More arcs
• Major arc- part of a circle that measures
between 180o and 360o.
(needs three letters to name)
A
(
(
ABC or CBA
B
• Semicircle- an arc whose endpts C
are the endpts of a diameter of the circle C
(OR ½ of a circle)
(need 3 letters to name)
S
Arc measures
• Measure of a minor arc- measure of its
central 
• Measure of a major arc- 360o minus
measure of minor arc
Ex: find the arc measures
(
E
m AB=
50o
(
m BC= 130o
(
180o
D
50o
130o
(
C
A m AEC= 180o
m BCA= 180o+130o
= 310o
OR 360o- 50o = 310o
B
Arc Addition Postulate
• The measure of an arc formed by two
adjacent arcs is the sum of the measures
of those arcs.
B
A
(
(
(
m ABC = m AB+ m BC
C
Congruency among arcs
• Congruent circles are two circles with the
same radius
• Congruent arcs- 2 arcs with the same
measure that are arcs of the same circle or
congruent circles!!!
(
Example
m AB=30o
(
A
m
DC=30o
E
(
(
AB @ DC
D
30o
C
30o
B
Ex: continued
(
m BD= 45o
m AE= 45o
BD @ AE
A
(
(
(
B
The arcs are the
same measure;
so, why aren’t
they @?
The 2 circles
are NOT @ !
C
45o
D
E
Lesson 6.3
Apply Properties of Chords
Page 198
Theorem 6.5
B
C
(
(
• In the same circle (or in congruent circles),
2 minor arcs are congruent if and only if
their corresponding chords are congruent.
A
AB @ BC iff
AB@ BC
Theorem 6.6
If one chord is a perpendicular bisector of another
chord, then the first chord is a diameter.
M
If JK is a  bisector
of ML, then JK is a
diameter.
K
J
L
Theorem 6.7
• If a diameter of a circle is  to a chord, then
the diameter bisects the chord and its arc.
E
D
C
G
F
(
(
If EG is  to DF,
then DC @ CF
and DG @ GF
(
Ex: find m BC
B
3x+11=2x+47
x=36
2(36)+47
72+47
119o
A
D
(
(
By thm 10.4
BD @ BC.
C
Theorem 6.8
In the same circle (or in @ circles), 2 chords are @
iff they are =dist from the center.
D
C
G
DE @ CB iff AG @ AF
F
A
E
B
Ex: find CG.
B
6
A
6
G
C
D
 CG = √13
7
6
CF @ CG
72=CF2+62
49=CF2+36
13=CF2
CF = √13
F
6
E