Section 9-3
Arcs and
Central Angles
Central angle
• An angle with its vertex
at the center of a circle.
Circle B
ABC is a central angle
ARC
• an unbroken part of a circle
AC
: read “arc AC”
Types of Arcs:
1. Minor Arc: less than 180
•
•
Measure is the same as its central angle
Named using two letters (Ex: AC )
2. Major Arc: more than 180
•
•
Measure is 360 minus the measure of its
central angle
m PQ
+ m
QR = (Ex:
m  PQR )
Named using
three
letters
3. Semicircle: equals 180
•
•
Endpoints of a diameter
Named using three letters
Adjacent Arcs
• Arcs in a circle that have
exactly one point in
common.
A
m AB and
=m90BD = 30
are adjacent arcs
C
B
D
Arc addition postulate
• The measure of the arc
formed by two adjacent arcs
is the sum of the measures
of these two arcs.
• Applies like segment addition postulate
m
PQ
+
m
QR
=
m
PQR

ABD
mmm
PQ
+
m
QR
=
m
AB
=
90
mPQ
PQ++ mmBD
QR= =30mPQR
PQR
QR
A
C
B
D
Congruent Arcs
• Arcs, in the same circle or in
congruent circles, that have
equal measures.
Theorem 9-3
• In the same circle or in
congruent circles, two minor
arcs are congruent if and
only if their central angles
are congruent.