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.

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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.

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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

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Two Tangents: angle+arc=180

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

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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.

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