10.2 & 10.4 – use properties of tangents and use inscribed angles and polygons
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10.2 & 10.4 – Use Properties of Tangents And Use Inscribed Angles and Polygons
Term Definition Picture
Central Angle
An angle whose vertex is the center of the circle
P
A
C
APC
Term Definition Picture
Minor Arc
Arc of a circle that is less than 180°
P
A
C
AC
Two letters:
Term Definition Picture
Major Arc
Arc of a circle that is more than 180°
P
A
C
ABC
3 letters:
B
Term Definition Picture
Semicircle
Arc of a circle that is 180°
P
A
C
ABC
3 letters:
B
Term Definition Picture
Congruent circles
Two circles with the same radius
Term Definition Picture
Congruent arcs
Arcs that have the same central angle
A B
CD
AB CD
The measure of a minor arc is the measure of its _____________ angle.central
P
A
Cx°
x°
MN73°
73°
73°
minor
NQ73°26°
26°minor
MP73°154°
26°minor
MRP73°206°
26°
107°
major
PN73°81°
26°
107°
minor
MNQ73°180°
26°
107°
semicircle
MRQ73°180°
26°
107°
Semicircle
MRN73°287°
26°
107°
major
10.4 – Use Inscribed Angles and Polygons
An angle whose vertex is on a circle and whose sides are chords of the circle
Inscribed angle:
An arc that is inside an inscribed angle
Intercepted Arc:
A polygon that has all of its vertices on a circle
Inscribed Polygon :
The circle that contains the vertices of a polygon
Circumscribed Circle:
The measures of an inscribed angle is ________ the measure of its ______________ arc.
halfintercepted
D = AB 2
x°
2x°
If two inscribed angles of a circle _____________ the same arc, then the angles are _____________.
interceptcongruent
D C
A ________ triangle is inscribed in a circle iff the _______________ is a diameter of the circle.
righthypotenuse
B is a right angle because it inscribes a semicircle.
A ____________________ can be inscribed in a circle iff its opposite angles are ______________.
quadrilateralsupplementary
mD + mF = 180°
mE + mG = 180°
Find the indicated measure.
=158 2
= 79°
Find the indicated measure.
=180 2
= 90°
180°
90°
Find the indicated measure.
= 40 2 = 80°
Find the indicated measure.
=
88°
92°
92 2
= 46°
Find the indicated measure.
=80 2
= 40°100°
80°
Find the indicated measure.
=56 2
= 28°
56°
Find the measure of A and C.
80°
mA =80 2
= 40°64°
mC =64 2
= 32°
Find the measure of A and C.
mA =146 2
= 73°
mC =62 2
= 31°
146°
62°
mPNO = 68 2
= 34°
mQNP = 62 2
= 31°
62°
= 62°
62°
= 130°
62°
= 112°
62°
112°
= 248°
62°
112°
Decide whether a circle can be circumscribed about the figure.
70 + 130 180
No,
Decide whether a circle can be circumscribed about the figure.
91 + 89 = 180
Yes,
91°
Decide whether a circle can be circumscribed about the figure.
115 + 63 180
No,
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
x = 72°
y + y = 180
2y = 180
y = 90°
Find the value of the variables.
4x = 84+44 2
8x = 128
x = 16°
7y = 152+44 2
14y = 196
y = 14°
44°
1 1
Find the value of the variables.
12x = 96+48 2
24x = 144
x = 6°
3y = 48+171 2
6y = 219
y = 36.5°
171°
1 1
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