Hochstetter_Denna_11_2_Arcs_and_Angle
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Vocabulary


11.2


Arcs and Chords
A
Central Angle:
 Angle with vertex at center of circle
Minor
Minor Arc:
Arc
Major
C entral
 Arc with central angle < 180º
Arc
P Angle
AB
AC B
 Named by 2 endpoints
Major Arc:
C
B
 Arc
A with
ith central
t l angle
l > 180º
Semicircle:
Whole Circle
 Arc whose endpoints are a diameter
= 360º total
 angle = 180º

Measure of an arc

Arc Addition Postulate
F
Minor Arc:
as central angle
 FG = 55º
 FH = 125º

 same

Semicircle:
 HFG

H
55
E
The measure of an arc formed by two
adjacent arcs is the sum of the two arcs.
 Similar
to segment and angle addition postulate
G
F
  FG
  _____

HF
= 180 º
Major Arc:
 GHF
A major arc or semicircle uses three endpoints
55
H
G
E
= 360º – minor arc = 360º - 55º = 305º
  ___
  FHJ

HF
J
DEF: Congruent Arcs

Two arcs of the same circle or congruent
circles are congruent if they have the
same measure
Chord Theorems: 1 of 4
 In the same circle or  circles, two minor arcs are 
iff their corresponding chords are  .
A
C
B
AB  BC iff AB  BC
Similar to “if sides, then angles”
“If Chords, then Arcs”
“If Arcs, then Chords”
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Hochstetter_Denna_11_2_Arcs_and_Angle
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Chord Theorems: 2 of 4

If a diameter of a circle is perp to a chord, then
the diameter bisects the chord and its arc.
3/10/2010
Chord Theorems: 3 of 4

If chord 1 is a perp bisector of chord 2,
then the chord one is a diameter
J
Given: JK is ┴ bisector of LM
So.... DE  EF, DG  GF
Then:
M
F
E
D
L
G
Chord Theorems: 4 of 4


In the same circle, or congruent circles,
two chords are congruent iff
they are equidistant from the center
K
In other words…
C
Remember: How do we measure distance?
 The
E
A
Y
3x + 4
X
D
segment that is perpendicular at that point
Ex: 1

arcs = 360
 13x - 30 = 360
 x = 30
A

Z
Find Arc YX
Ex 2:
B
C
A
57
 94º


Find Arc XZY
 360º
Find:
BC =
57º
CD =
180º – 57
180
57º = 123
123º
BD C = 360º – 57º = 303º
Find Arc YZ
 162º
B
F
 Sum
6x - 18
4x - 16
Solve for x
AB  CD iff EF  EG
G
D
- 94º = 266º
2
Hochstetter_Denna_11_2_Arcs_and_Angle
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Ex 3 & 4:
B
Given: EG = EF
CD= 10
Find: AB
E
D
G
E
D
F
F
C
C
A
3/10/2010
G
Given: DE = EF = 5
CG = 8
Find: BG
B
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