Section 10-2
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”
Three Types of Arcs:
1.Minor Arc: less than180
• Measure is the same as
its central angle
• Named using two letters
(Ex:
)
AC
2. Major Arc: more than180
• Measure is 360 minus the
measure of its associated
minor arc
• Named using three letters
(Ex:
)
= m  PQR
3. Semicircle: equals 180
• Endpoints of the arc are
the 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 the two arcs.
• Applies like segment addition postulate
A
C
B
D
m
PQ
+
m
QR
=
m
PQR

mmm
PQ
+
m
QR
=
m
AB
=
90
mPQ
PQ++ mmBD
QR= =30mABD
PQR
QR
PQR
Congruent Arcs
• Two arcs of the same circle
or of congruent circles are
congruent if they have the
same measure.