Angles and Arcs
Section 10-2
central angle – an angle whose
vertex is at the center of a circle
L
C
U
Y
LCY is a central angle.
Theorem 10-1
In
the same or in congruent
circles, two arcs are
congruent iff their
corresponding central angles
are congruent.
Sum of Central Angles
The sum of the measures of
the central angles of a circle
with no interior points in
common is 360o.
L
LUY is a
major arc
C
U
LY is a minor arc
Y
A minor arc consists of its endpoints and
all points on the circle interior to the
angle.
A major arc uses 3 letters to name the arc
and consists of its endpoints and all points
on the circle exterior to the angle.
X
AXB is a semicircle
A
B
The measure of a semicircle is 180o.
Definition of Arc Measure
The measure of a minor arc is the
measure of its central angle.
The measure of a major arc is 360
minus the measure of its central angle.
P
100o
C
R
m PM = 100o
M
m PRM = 260o
Arc Addition Postulate
The measure of an arc formed by 2
adjacent arcs is the sum of the
measures of the 2 arcs. That is, if
Q is a point on PR, then
P
m PQ + m QR = m PQR.
Q
R
Arc Length
The arc length is different from the
degree measure of an arc. Suppose
a circle was made of string. The
length of the arc would be the
linear distance of that piece of
string representing the arc.
Arc Length =
angle
x
Circumfere
nce
o
360
Concentric circles lie in the same
plane and have the same center,
but have different radii.
All circles are similar, so concentric
circles are also similar.
Joke Time
What flower grows between your
nose and your chin?
Tulips
Why were Goldilocks and the Big
Bad Wolf in the same house?
It was two-story