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10.2 & 10.4 – Use Properties of Tangents
And Use Inscribed Angles and Polygons
Term
Definition
Picture
A
C
Central
Angle
An angle
whose
vertex is the
center of
the circle
P
APC
Term
Definition
Picture
A
C
Minor Arc
Arc of a
circle that
is less than
180°
P
Two letters:
AC
Term
Definition
Picture
A
C
Major Arc
Arc of a
circle that
is more
than 180°
P
B
3 letters:
ABC
Term
Definition
Picture
A
Semicircle
Arc of a
circle that
is 180°
P
B
C
3 letters:
ABC
Term
Congruent
circles
Definition
Two circles
with the
same radius
Picture
Term
Congruent
arcs
Definition
Arcs that
have the
same
central
angle
Picture
A
B
D
C
AB  CD
The measure of a minor arc is the
central
measure of its _____________
angle.
A
x°
x°
P
C
MN
73°
minor
73°
73°
NQ
26°
73°
minor
26°
MP
154°
73°
minor
26°
MRP
206°
major
73°
107°
26°
PN
81°
minor
73°
107°
26°
MNQ
180°
semicircle
73°
107°
26°
MRQ
180°
Semicircle
73°
107°
26°
MRN
287°
major
73°
107°
26°
10.4 – Use Inscribed Angles and
Polygons
Inscribed angle: An angle whose vertex is on
a circle and whose sides are
chords of the circle
Intercepted Arc: An arc that is inside an
inscribed angle
Inscribed Polygon : A polygon that has all of its
vertices on a circle
Circumscribed Circle: The circle that contains
the vertices of a polygon
half
The measures of an inscribed angle is ________
the measure of its ______________
arc.
intercepted
2x°
x°
D = AB
2
intercept
If two inscribed angles of a circle _____________
the same arc, then the angles are _____________.
congruent
D  C
A ________
right triangle is inscribed in a circle iff
the _______________
is a diameter of the circle.
hypotenuse
B is a right angle
because it inscribes a
semicircle.
quadrilateral
A ____________________
can be inscribed in a
circle iff its opposite angles are ______________.
supplementary
mD + mF = 180°
mE + mG = 180°
Find the indicated measure.
158
=
= 79°
2
Find the indicated measure.
180
=
= 90°
2
90°
180°
Find the indicated measure.
= 40  2 = 80°
Find the indicated measure.
88°
92°
92
=
= 46°
2
Find the indicated measure.
80
=
= 40°
2
100°
80°
Find the indicated measure.
56
=
= 28°
2
56°
Find the measure of A and C.
80
mA =
= 40°
2
64°
80°
64
mC =
= 32°
2
Find the measure of A and C.
146°
146
mA =
= 73°
2
62
mC =
= 31°
2
62°
68
mPNO = 2 = 34°
62
mQNP = 2 = 31°
62°
= 62°
62°
= 130°
62°
= 112°
112°
62°
= 248°
112°
62°
Decide whether a circle can be circumscribed
about the figure.
No,
70 + 130  180
Decide whether a circle can be circumscribed
about the figure.
Yes,
91 + 89 = 180
91°
Decide whether a circle can be circumscribed
about the figure.
No,
115 + 63  180
Find the value of the variables.
5x + 110 = 180
5x = 70
x = 14°
2y + 104 = 180
2y = 76
y = 38°
Find the value of the variables.
x + 108 = 180
y + y = 180
x = 72°
2y = 180
y = 90°
Find the value of the variables.
44°
4x = 84+44
1
2
7y = 152+44
1
2
8x = 128
14y = 196
x = 16°
y = 14°
Find the value of the variables.
171°
12x = 96+48
1
2
24x = 144
x = 6°
3y = 48+171
1
2
6y = 219
y = 36.5°