Transcript Document
Circles
Parts of a Circle
A
B
C
D
Radius - segment from center pt to a point on the circle.
Ex. AC, BC, DC are all radiuses
Parts of a Circle
Chord - segment whose endpoints are on the circle.
Ex. PR, PS, are chords
Diameter - a chord that passes through the center point of a circle.
Ex. PR is a diameter
Parts of a Circle
Arc - Part of a circle's edge
0
Minor Arc - an arc that is less than 180
- use two letters to label a minor arc. Ex.
0
Major Arc - an arc that is more than 180
- use three letters to label major arc. Ex.
Parts of a Circle
Central angle - an angle whose vertex is at the center of the circle.
Ex. <APB
Intercepted Arc – arc that is cut off by the sides of an angle.
Ex. arc AB is the intercepted arc
Parts of a Circle
1
Inscribed angle - an angle whose vertex is on the circle.
Ex. <1 is an inscribed angle.
A
Put the answers to the following
on your notesheet:
Radius
Diameter
C
Major Arc
Minor Arc
L
T
P
Chord
Central angle
Inscribed Angle
Central Angle = Intercepted Arc
A
<1= 105 (vertical angles), <2=75 (forms a line
with 105), <3 = 75 (forms a line with105).
Therefore arc BD = 105, arc AB = 75, arc DC = 75
105
A
75
B
B
1
In the picture at right arc AB = 80, so angle 1 = 80
because <1 is a central angle
In the picture at right arc AC = 105,
because its central angle is 105.
80
105
2
1 3
105
105
C
75
D
Central Angle = Intercepted Arc
Put these on your notesheet
1 - Find x
A
2 - find x
30
E
110
x
A
C
x
L
D
3 - find arc AB
B
4 - find angles 1, 2, 3
A
B
100
B
A
127
1
2
D
L
C
3
D
132
Central Angle = Intercepted Arc
Put these on your notesheet
1 - Find x
A
x110
2 - find x
E
30
A
30
110
C
x
30
L
X=110 because
Central angle = intercepted arc
D
B
X=30 because
Central angle = intercepted arc
so <ECA = 30, x is vertical to
<ECA so x=30
Central Angle = Intercepted Arc
3 - find arc AB
B
Put these on your notesheet
53
4 - find angles 1, 2, 3
A
100
A
53
127
127
D
Arc AD=127, arc AB and arc
AD form a semicircle (180
degrees) 180-127=53
Or you could say the
unlabeled angle next to 127
is 53 and then the arc is 53
100
1 48
3
2
80C
132
L
B
D
132
<1=100 b/c it is central to arch AB
<2=80 b/c it forms a line with <1 (180100 = 80)
<3=48 b/c arc AD is 48 (180-132)
Place these problems on your HALF SHEET OF PAPER
Inscribed Angle = (Intercepted Arc)/2
Or
Intercepted Arc = 2(Inscribed Angle)
70
A
A
B
35
1
C
Above arc AB = 70,
so angle 1 = 35
because <1 is an
inscribed angle
142
98
98
1
B
49
713 2 460
C
Above arc AB=98, so <1=98 (central
angle=arc), <2=49 (inscribed angle =
arc/2), <4=60 (inscribed angle = arc/2)
<3=71 (180-49-60), arc AC=142
(arc=2(inscribed angle)
Inscribed Angle = (Intercepted Arc)/2
Put these on your notesheet
EX1 - Find x
A
EX2 - Find arc AB, A
and x
80
x
1
C
B
B
x
R
angle 1 = 90
EX3 - Find arc AB and arc ATB
T
4 - find angles 1, 2, 3
100
A
B
56
A 145
D
B
3 1 2
L
132
Inscribed Angle = (Intercepted Arc)/2
Put these on your notesheet
EX1 - Find x
A
90
80
x40
EX2 - Find arc AB, A
and x
B
x = 40 because an
inscribed angle
equals half the
intercepted arc
B
1
C
45x
R
angle 1 = 90
Arc AB=90 because an arc equals
its central angle.
Since angle x is inscribed and
Intercepts arc AB, x = AB/2=45
Inscribed Angle = (Intercepted Arc)/2
EX3 - Find arc AB and arc ATB
T
290
4 - find angles 1, 2, 3
100
A
B
56
A 145
B
70
Arc ATB is a major arc (more
than 180). Arc ATB=290 {because
the arc is twice its inscribed
angle of 145}
AB=170, because AB and ATB
make the whole circle so
360-290=70
363 50 28
1 2
L
D
132
<1=50because it is an inscribed
angle and half arc AB
<2=28 because it is an inscribed
angle and half arc BD
<3=36, Arc AL=72 because
360-100-50-132=72. <3 is
inscribed so it is 72/2
Place these problems on your HALF SHEET OF PAPER