Central & Inscribed Angles

​How many squares?

Bellringer

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Central & Inscribed Angles

Dr. Tom Giles

An inscribed angle, (B), is an angle drawn inside of a circle such that...

• its vertex lies on the circumference of a circle and

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• its sides intercept the circle (A and C).

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​Inscribed Angles

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Multiple Choice

An angle in a circle with vertex on the circle itself

• Angle
• Central angle
• Inscribed angle
• Chord

Multiple Choice

Angle a is called ___ angle.

• central

• inscribed

The Central Angle of a circle is an angle whose...

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• vertex is at the center (0) of a circle and...

• ​The two arms form two radii of the circle

• intersecting the arc of the circle at different points

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​Central Angle

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Multiple Choice

An angle in a circle with vertex on the center of the circle called

• Angle
• Central angle
• Inscribed angle
• Chord

Note that the Central Angle (AOB) cuts the circle in two points...

• at Point A

• at point B

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​The Arc AB is called the...

Intercepted Arc

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Central Angle = Intercepted Arc​

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​Intercepted Arc, Central angle and Inscribed Angle

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Inscribed Angle = 1/2( Intercepted Arc )​

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The Central angle angle and the Inscribed Arc have the same measure​.

So, if the Central angle = 40^o

​The Intercepted Arc measure = 40^o

​Angle R = Arc AL

​Central Angles and Intercepted Arc Measure

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The Intercepted Arc is Twice the measure of the Inscribed Angle.

So, if the Inscribed angle = 20^o

​The Intercepted Arc measure = 40^o

​Angle C = 1/2 Arc AL

​Inscribed Angles and Intercepted Arc Measure

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Multiple Choice

An angle in a circle with vertex on the center of the circle

• Central angle
• Angle
• Inscribed angle
• Circle

Multiple Choice

An angle in a circle with vertex on the circle itself

• Angle
• Central angle
• Inscribed angle
• Chord

Multiple Choice

Find the measure of arc AB.

• 17
• 34
• 68
• 146

Multiple Choice

What is the measure of arc FH?

• 70

• 35

• 140

• 88

Multiple Choice

What is the measure of angle K and angle M?

• $$m\angle K=100\ \ \ \ \&\ \ \ m\angle M=100$$

• $$m\angle K=50\ \ \ \ \&\ \ \ m\angle M=50$$

• $$m\angle K=100\ \ \ \&\ \ \ m\angle M=50$$

• $$m\angle K=50\ \ \ \&\ \ \ m\angle M=100$$

Multiple Choice

Which number best represents an inscribed angle?

• 1

• 2

• 8

• 9

Multiple Choice

Find x.

• 51

• 25.5

• 102

• 67

Multiple Choice

Find x.

• 48

• 24

• 96

• 42

Multiple Choice

How many degrees are in the Central Arc GE?

• A

• B

• C

• D

Multiple Choice

How many degrees are in the Inscribed Angle U?

• A
• B
• C
• D

Multiple Choice

How many degrees are in the Inscribed Angle Q?

• A
• B
• C
• D

Multiple Choice

Which number best represents an inscribed angle?

• 1

• 2

• 8

• 9

Multiple Choice

What is m∠ACB?

• 67.5°
• 90°
• 22.5°
• 45°

Multiple Choice

Find the measure of arc AB.

• 17
• 34
• 68
• 146