Cavalieri's Principle Extended to Circles

4.1b Lesson: Inscribed Angles in Circles

SOL G.11.a

I can describe arc measures associated with inscribed angles.

Open Ended

How do you know the given image is a circle?

How can you verify or prove that it is a circle?

Show your work!

Multiple Choice

Find the measure of Arc TW.

• 319º

• 41º

• 360º

• 82º

Inscribed Angles

Inscribed Angles are angles with their vertex ON the circle.

They look like this ------------------>

Here are some NON-examples. These are NOT inscribed angles.

Inscribed Angles vs. Central Angles

Multiple Choice

What is the measure of arc PR ?

• 360º

• 45º

• 90º

• 180º

Inscribed Angles vs. Central Angles

Open Ended

In general, what can you tell about the measure of

$$\angle PQR$$  compared to 

Take a look at this animation similar to our Circle O

Inscribed Angles have a measure that is exactly HALF of the measure of their intercepted arc.

Multiple Choice

What is the measure of

$$\angle EDF$$  ?
(click image to enlarge)

• 120º

• 60º

• 180º

• 360º

Multiple Choice

What is the measure of

$$\angle XWE$$  ?
(click image to enlarge)

• 180º

• 112º

• 56º

• 360º

Multiple Choice

Find the measure of the

$$arc\ \overline{DC}$$  .
(click image to enlarge)

• 124º

• 62º

• 31º

• 360º

Multiple Choice

Find the measure of the

$$arc\ \overline{XW}$$ .
(click image to enlarge)

• 56º

• 180º

• 360º

• 106º

Poll

Choose the option that best describes you.

• I understand inscribed angles and arcs completely so far. I could answer more difficult questions on my own.

• I think I understand inscribed angles and arcs, but I need more practice right now.

• I need to be retaught the entire lesson.

Multiple Choice

When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees.  What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

• 40
• 35
• 55
• 69

Multiple Choice

What is the area of the shaded region? Round to the nearest hundredth.

• 8.37

• 2.09

• 33.49

• 4.19

Multiple Choice

If O is the center of the circle, find the measure of central angle x.

• x = 160 degrees

• x = 40 degrees

• x = 80 degrees

• x = 360 degrees

Multiple Choice

• A
• B
• C
• D

Multiple Choice

8.

• 67.5°
• 90°
• 22.5°
• 45°

Multiple Choice

Find the measure of arc QR

• 106
• 85
• 113
• 78

Circumscribed Angles and Tangent

By Mrs. Swain

​On a circle, a tangent is a line that touches, but that does not intersect the circle.

In the picture, the red line is a Tangent​

​

Unit 12

​What is Tangent?

Unit 12​

​When two tangents touch

​

Fill in the Blank

What is the value of $$\overline{KL}$$  ?

Fill in the Blank

What is the value of $$\overline{JQ}$$  ?

Fill in the Blank

What is the value of $$\overline{PM}$$  ?

Fill in the Blank

What is the Perimeter of Triangle KQM?

​Tangent and the radius (purple line) will always form a 90 degree angle.

​

Unit 12.

​What is Tangent?

Unit 12

​Find the missing length

Multiple Choice

What is the value of x?

• 12

• 17.5

• 6

• 1.9