G.11 Circles- Inscribed Angles, Arcs, and Chords

Inscribed Angles in Circles

SOL G.11.a

I can describe arc measures associated with inscribed angles.

Central angle: angle=arc

Central angles have a vertex at the center of the circle. The arc created by the two radii is equal to the angle.

Fill in the Blank

What is x?

Inscribed Angle: angle=1/2*arc or arc=2*angle

Inscribed angles must have a vertex touching the circle. The angle is half of the outside arc or the arc is twice the angle inside.

Fill in the Blank

What is x?

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

Fill in the Blank

Solve for x. Just type in the numeric value.

Fill in the Blank

Find $$m\angle POQ$$

Just type in the numeric value.

Two Tangents: angle+arc=180

Two tangents create an angle and an arc (small arc). These two added together always equal 180.

Fill in the Blank

What is x equal to?

External: angle=1/2(big arc - little arc)

When two secants meet outside of a circle, the angle is equal to half of the different of the arcs.

Fill in the Blank

What is the measure of the missing angle?