Inscribed Angle Theorem

Angle ABC is called an inscribed angle. Move point C around and see what happens to angle ABC. Then move points B around and see what happens to angle ABC

When moving point B does the angle change?

No Yes

When moving point C does the angle change?

Yes No

Now we will connect some more points and create a new angle ADC which is called the central angle

What do you think the central angle is in the circle shown above?

The central angle was 90

Play around with the positioning of points B and D. See if you can find a relationship between the inscribed angle and central angle

What kind of relationship did you notice between the central angle and the inscribed angle?

Review

The following are some problems for you to try

Find the measurement of the central angle

What is the measurement of the central angle

132 107 73 146

Find the measurement of the inscribed angle

What is the measurement of the inscribed angle

112 52 56 68

Find the measurement of the central angle

What is the measurement of the central angle

a/2 a[math]^2[/math] a 2a

Now that you have gone through this whole activity. What is the relationship between the central angle and the inscribed angle?

The central angle and the inscribed angle are the same The central angle is half of the inscribed angle The central angle is double the inscribed angle There is not relationship between the central angle and the inscribed angle

Inscribed Angle Theorem

Angle ABC is called an inscribed angle. Move point C around and see what happens to angle ABC. Then move points B around and see what happens to angle ABC

Now we will connect some more points and create a new angle ADC which is called the central angle

The central angle was 90

Play around with the positioning of points B and D. See if you can find a relationship between the inscribed angle and central angle

Review

Find the measurement of the central angle

Find the measurement of the inscribed angle

Find the measurement of the central angle

Information: Inscribed Angle Theorem