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10.2 Arcs and Chords
Central angle
Minor Arc
Major Arc
Central angle
A central angle is an angle which vertex is the center of a circle
Minor Arc
An Arc is part of the circle.
A Minor Arc is an arc above the central angle if the central angle is less then 180°
Major Arc
A Major Arc is an arc above the central angle if the central angle is greater then 180°
ADBArcMajor
ABArcMinor
Semicircle
If the central angle equals 180°, then the arc is a semicircle.
Semicircle
If the central angle equals 180°, then the arc is a semicircle.
Measure of an Arc
The measure of an Arc is the same as the central angle.
30AC
Measure of an Arc
The measure of an Arc is the same as the central angle.
120AB
240
120360
ADB
ADB
D
A
B
Postulate: Arc Addition
Arcs can be added together.
110
27
83
QR
RP
QP
83
27
Congruent Arcs
If arcs comes from the same or congruent circles, then they are congruent if then have the same measure.
A
B
KG
85
85KGAB
Congruent chords Theorem
In the same or congruent circles, Congruent arcs are above congruent chords.
CDAB
CDAB
ifonlyandif
Theorem
If a diameter is perpendicular to a chord , then it bisects the chord and its arc.
BCAC
BEAE
Theorem
If a chord is the perpendicular bisector of another chord (BC), then the chord is a diameter.
ECBE
DCBD
Solve for y
140
90
AB
AMOm
y2
Solve for y
140
90
AB
AMOm
y2
35
702
y
y
Theorem
In the same or congruent circles, two chords are congruent if and only if they are an equal distance from the center.
RSPQ
BOAOSince
,
Solve for x, QT
UV = 6; RS = 3; ST = 3
Solve for x, QT
UV = 6; RS = 3; ST = 3
x = 4,
Since Congruent
chord are an
equal distance
from the center.
Solve for x, QT
UV = 6; RS = 3; ST = 3
x = 4,
5916
34 222
QT
QT 4
Find the measure of the arc
Solve for x and y
52
52
62 y
10x
Find the measure of the arc
Solve for x and y
52
52
62 y
10x
23
246
)62(52
44
1052
y
y
y
x
x
Homework
Page 607 – 608
# 12 - 38
Homework
Page 608 -609
# 39 – 47,
49 – 51,
69, 76 - 79
