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

Place these problems on your HALF SHEET OF PAPER

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

502836

Place these problems on your HALF SHEET OF PAPER

THE END