8/8/2019 Presentation 7.4 Inscribed Angles
1/23
8/8/2019 Presentation 7.4 Inscribed Angles
2/23
1/1/2011
Vocabulary
inscribed angle
intercepted arc
8/8/2019 Presentation 7.4 Inscribed Angles
3/23
1/1/2011
An inscribed angle is an angle whose vertex
is on a circle and whose sides contain chords
of the circle.
intercepted
arc
The arc that lies in the interior of an inscribed
angle and has endpoints on the angle is called
the intercepted arc of the angle.
inscribed
angle
8/8/2019 Presentation 7.4 Inscribed Angles
4/23
1/1/2011
Ifanangleisinscribedinacircle,thenits
measureis
C68 Inscribed AngleConjecture
m ADB = m AB1
2
C
A
BD
halfthe measureofits
interceptedarc.
8/8/2019 Presentation 7.4 Inscribed Angles
5/23
1/1/2011
Find the measure of the QTS.
Finding Measuresof Arcsand Inscribed Angles
110
R
T Q
mQRS = mQTS
=1
2
= mQTS
220 = mQTS
S
C
110
8/8/2019 Presentation 7.4 Inscribed Angles
6/23
1/1/2011
Find the measure ofQRS.
Finding Measuresof Arcsand Inscribed Angles
165mQRS = mQTS
=1
2
mQRS =( )
R
T Q
S
C
165mQRS = 82.5
8/8/2019 Presentation 7.4 Inscribed Angles
7/23
1/1/2011
100
m NMP = 50
N
P
M 100C
Find the measure ofNMP.
Finding Measuresof Arcsand Inscribed Angles
m NMP = mNP
=1
2100
m NMP = ( )
8/8/2019 Presentation 7.4 Inscribed Angles
8/23
1/1/2011
N
P
M
235
C
If mNMP = 235, then find the measure
ofNMP
Finding Measuresof Arcsand Inscribed Angles
125
m NMP = 62.5
m NMP = ( )
=1
2
mNP = 360 mNMP
mNP = 360 - 235
mNP = 125
m NMP = mNP
8/8/2019 Presentation 7.4 Inscribed Angles
9/23
1/1/2011
W
X
Z
Find the measure ofZWX
Finding Measuresof Arcsand Inscribed Angles
m ZCX = m ZX
m ZWX =360 - 115
= m ZX115
m ZWX = 245
C
115
=
MAJOR ARC= 360 minorarc
8/8/2019 Presentation 7.4 Inscribed Angles
10/23
1/1/2011
C69
A
D
CB
C
$ D
Iftwoinscribedanglesofa
circleinterceptthesamearc,
thentheanglesare
congruent.
8/8/2019 Presentation 7.4 Inscribed Angles
11/23
1/1/2011
You decide that the
middle of the sixth row
has the best viewing
angle, point F.
THEATER DESIGN When you go to the movies, you want to be close to the
movie screen, but you dont want to have to move your eyes too much
to see the edges of the picture.
Usingthe Measureofan Inscribed Angle
moviescreenE G
F
IfEand Gare the ends of the screen and you are at F, mEFGis
called yourviewing angle.
If someone is sitting
there, where else can
you sit to have the
same viewing angle?
8/8/2019 Presentation 7.4 Inscribed Angles
12/23
1/1/2011
SOLUTION
Draw the circle that is determined by the
endpoints of the screen and the sixth rowcenter seat.
Any other location on the circle will have the
same viewing angle.
Why?
8/8/2019 Presentation 7.4 Inscribed Angles
13/23
1/1/2011
Ifalloftheverticesofapolygonlieonacircle,thepolygon
isinscribed inthecircleandthecircleiscircumscribed
aboutthepolygon.Thepolygonisaninscribedpolygonandthecircleisacircumscribedcircle. Thepolygonissaid
to be cyclic.
8/8/2019 Presentation 7.4 Inscribed Angles
14/23
1/1/2011
A righttriangleisinscribedinacircleiffthehypotenuseisadiameterofthecircle.
C
A
B
C70
Forexample,
If ACisadiameterofthecircle,thenB isarightangleand
See GSP 10.5A
ifB isarightangle,then
ACisadiameterofthecircle.
8/8/2019 Presentation 7.4 Inscribed Angles
15/23
1/1/2011
Ex: A, B, C, andDlieonacircle,
A
D
B
C
180mD +mB =
360mABC +mADC =
8/8/2019 Presentation 7.4 Inscribed Angles
16/23
1/1/2011
A quadrilateralcanbeinscribedinacircleifand
onlyifitsoppositeanglesaresupplementary.
C
E
D
F
G
C71
Ex: D, E, F, and G lieonC,
iff m D + m F = 180 and
m E+ m G = 180.
8/8/2019 Presentation 7.4 Inscribed Angles
17/23
1/1/2011
Is AC a diameter?ABCD is an inscribed quadrilateral inP.
C
B
D
53
P
mABC =
mCPD=
mBCD =
mADB =
mBCA =
mDBC =
180
26.5
307
63.5
106
127
?
If mBC = 53, then find ... A 53
8/8/2019 Presentation 7.4 Inscribed Angles
18/23
1/1/2011
In the diagram, ABCD is inscribed in P.
Find the measure of each angle.
P
B
C
D
A
2y
3y
5x
3x
8/8/2019 Presentation 7.4 Inscribed Angles
19/23
1/1/2011
ABCD is inscribed in a circle,
so opposite angles are
supplementary.
PB
C
D
A2y
3y
5x
3x
3x+
3y=
180 5x+
2y
=180
15x+ 6y= 540
-6x- 6y=
-360
*3
*-2
9x = 180
x =20
3(20) + 3y= 180
60 + 3y = 180
3y=
120y = 40
8/8/2019 Presentation 7.4 Inscribed Angles
20/23
1/1/2011
x= 20 andy= 40
mA = 2y= 2(40)
= 80
mB = 3x
= 3(20)= 60
m
C = 5x= 5(20)
=100
m
D = 3y= 3(40)
= 120
PB
C
D
A2y
3y
5x
3x
8/8/2019 Presentation 7.4 Inscribed Angles
21/23
1/1/2011
C72:Parallel lines interceptcongruent arcs on a circle.
8/8/2019 Presentation 7.4 Inscribed Angles
22/23
1/1/2011
1. Givenacirclewith
centerpoint P.B
D
F
E
CA
H
P
G
2. Thecircleisdivided
into8congruent
arcs.
3. Thepointsoftheoctagonare A, B,
H,labeled
counter-clockwise.
4. Connectevery 3rd
pointwitha
diagonal, AD, DG,
GB, BEuntilyou
returntopoint A.
8/8/2019 Presentation 7.4 Inscribed Angles
23/23
1/1/2011
mDAF = ( )90mDAF = 45
Find mDAF
360/8 = 45
45*2 = 90
F
mDAF = mDF
D
E
CB
A
H
P
G
Top Related