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°
Minor Arc AB
Major Arc ADB
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.
AC  30
Measure of an Arc
The measure of an Arc is the same as the
central angle.
AB 120
A
B
D
ADB  360  120
ADB  240
Postulate: Arc Addition
Arcs can be added together.
83
QP  83
RP  27
27
QR  110 
Congruent Arcs
If arcs comes from the same or congruent
circles, then they are congruent if then
have the same measure.
B
A
AB  KG
85
85
G
K
Congruent chords Theorem
In the same or congruent circles, Congruent
arcs are above congruent chords.
AB  CD
if and only if
AB  CD
Theorem
If a diameter is perpendicular to a chord ,
then it bisects the chord and its arc.
AE  BE
AC  BC
Theorem
If a chord is the perpendicular bisector of
another chord (BC), then the chord is a
diameter.
BD  DC
BE  EC
Solve for y
mAMO  90
AB  140
2y
Solve for y
mAMO  90
AB  140
2 y  70
y  35
2y
Theorem
In the same or congruent circles, two chords
are congruent if and only if they are an
equal distance from the center.
Since AO  BO,
PQ  RS
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,
QT  4  3
2
2
2
QT  16  9  5
4
Find the measure of the arc
Solve for x and y
 x 10
52
52
2 y  6
Find the measure of the arc
Solve for x and y
52  x  10
x  44
52  (2 y  6)
46  2 y
y  23
 x 10
52
52
2 y  6
Homework
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# 12 - 38
Homework
Page 608 -609
# 39 – 47,
49 – 51,
69, 76 - 79