Central/Inscribed Angles & Parabolas

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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​Some text here about the topic of discussion.

​Inscribed Angles

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Multiple Choice

Angle a is called ___ angle.

• central

• inscribed

Multiple Choice

An angle in a circle with vertex on the circle itself

• Angle
• Central angle
• Inscribed angle
• Chord

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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​Intercepted Arc

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The measure of the central angle and the Arc are the same​.

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So if central angle = 30^o

​The Arc measure = 30^o

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​Some text here about the topic of discussion.

​Central Angles and Intercepted Arc Measure

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Central Angle = Intercepted Arc​

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​Some text here about the topic of discussion.

​Intercepted Arc, Central angle and Inscribed Angle

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Central Angle = 2( Intercepted Arc )​

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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

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

What is the measure of arc GE ?

• A

• B

• C

• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• 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

Parabola Basics

The vertex is the turning point of a parabola. Here, it is called a maximum point because it's the highest the ball goes

Multiple Choice

Quick review question: What is (x + 3)(x + 5)?

(Standard Form for Quadratic Equation

$$ax^2+bx+c=0$$ )

• 3x² + 2x + 15

• x² + 15

• x² + 8

• x² + 8x + 15

1. a tells you the amplitude (width) and if the parabola is positive or negative

2. b is the slope of the parabola

3. c is the y-intercept

All parabolas have symmetry

• The "axis of symmetry" cuts right down the middle and intersects the vertex

• It has an equation like any other vertical line

• x = 6

The vertex is the turning point

Minimum and Maximum points are different styles of vertex

Some parabolas

Open Upward (Minimum Vertex)

Some parabolas

Open Down (Maximum Vertex)

Multiple Choice

What is the maximum point of this parabola?

• (3, 5)

• (5, 3)

• (5, 0)

• (1, 0)

Multiple Choice

What is the minimum point of this parabola?

• (0, 7)

• (2, 3)

• (-2, 3)

• (3, 5)

The vertex can also be a minimum point.

Multiple Choice

When you throw a basketball through the air, the path it follows is a parabola. The parabola opens...

• UP

• DOWN

X-intercepts AKA Zeros

• Zeros is another name for x-intercepts because the y-coordinate there is 0

• Parabolas can have 0, 1, or 2 zeros, x-intercepts, roots, or solutions

• Most real-world stuff has two