Circles What will we learn - Parts of a circle including radius, diameter, arcs, angles - How to find arc measures - How to find angle measures
Dec 27, 2015
Circles
What will we learn- Parts of a circle including radius, diameter,
arcs, angles- How to find arc measures - How to find angle measures
Parts of a Circle
A
BC
D
Radius - segment from center pt to a point on the circle. Ex. AC, BC, DC are all radiuses
Diameter - a chord that passes through the center point of a circle. Ex. PR is a diameter
Chord - segment whose endpoints are on the circle. Ex. PR, PS, are chords
Parts of a Circle
Minor Arc - an arc that is less than 1800
- use two letters to label a minor arc. Ex.
Major Arc - an arc that is more than 1800
- use three letters to label major arc. Ex.
Arc - Part of a circle's edge
Parts of a Circle
Central angle - an angle whose vertex is at the center of the circle.
Ex. <APB
Parts of a Circle
Intercepted Arc – arc that is cut off by the sides of an angle.
Ex. arc AB is the intercepted arc
Inscribed angle - an angle whose vertex is on the circle.
Ex. <1 is an inscribed angle.
1
Parts of a Circle
Put the answers to the following on your notesheet:
Radius
Diameter
Major Arc
Minor Arc
Chord
Central angle
Inscribed Angle
T
A
P
L
C
Central Angles
Central Angle = Intercepted Arc
80
BA
1In 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.
B
A
105 C
D
32
1<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
105
105 75
75
B
30 A
Cx
D
E1 - Find x
2 - find x
3 - find arc AB
x 110
A
127
A
D
B
L
Central AnglesCentral Angle = Intercepted Arc Put these on your
notesheet
B100
12 3C
A
4 - find angles 1, 2, 3
D
L 132
B
30 A
Cx
D
E1 - Find x
2 - find x
x 110
A
L
Central AnglesCentral Angle = Intercepted Arc
X=110 because Central angle = intercepted arc
Put these on your notesheet
X=30 because Central angle = intercepted arc so <ECA = 30, x is vertical to <ECA so x=30
30
30
110
3 - find arc AB
127
A
D
B
Central AnglesCentral Angle = Intercepted Arc Put these on your
notesheet
Arc AD=127, arc AB and arc AD form a semicircle (180 degrees) 180-127=53Or you could say the unlabeled angle next to 127 is 53 and then the arc is 53
<1=100 b/c it is central to arch AB<2=80 b/c it forms a line with <1 (180-100 = 80)<3=48 b/c arc AD is 48 (180-132)
B100
12 3C
A
4 - find angles 1, 2, 3
D
L 132
53
127
53
10080
132
48
Inscribed AnglesInscribed Angle = (Intercepted Arc)/2
OrIntercepted Arc = 2(Inscribed Angle)
70
BA
1
C
Above arc AB = 70, so angle 1 = 35 because <1 is an inscribed angle
98
BA
4C
3 2
1 120
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)
35
98
496071
142
A
B
80
x
EX1 - Find x
EX2 - Find arc AB, and x
A
BC R
angle 1 = 90
1 x
A
B
T
145
Inscribed AnglesInscribed Angle = (Intercepted Arc)/2
EX3 - Find arc AB and arc ATB
Put these on your notesheet
B100
1 23
A
4 - find angles 1, 2, 3
D
L 132
56
A
B
80
x
EX1 - Find x
EX2 - Find arc AB, and x
A
BC R
angle 1 = 90
1 x
Inscribed AnglesInscribed Angle = (Intercepted Arc)/2 Put these on your
notesheet
x = 40 because an inscribed angleequals half the intercepted arc
40
Arc AB=90 because an arc equalsits central angle.Since angle x is inscribed andIntercepts arc AB, x = AB/2=45
90 4
5
A
B
T
145
Inscribed AnglesInscribed Angle = (Intercepted Arc)/2 EX3 - Find arc AB and arc
ATB B100
1 23
A
4 - find angles 1, 2, 3
D
L 132
290
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
70<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 because360-100-50-132=72. <3 is inscribed so it is 72/2
56
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