​ Finding the measure of the missing inscribed
angle

More Circle Vocabulary

There are 3 types of intersections that we will look at...

and the 3 different formulas associated with them.

Intersection #1 - Angle formed ON the circle

Intersection #1 - ON the circle

When two 'lines' intersect ON a circle, we see a few important relationships.

1. The angles formed are a linear pair (add to 180º).

2. The two arcs formed add to 360º.

3. The intercepted arcs of each angle are DOUBLE the measure of the angle.

Intersection #1 - ON the circle

When two 'lines' intersect ON a circle, we see a few important relationships.

1. The angles formed are a linear pair (add to 180º).

2. The two arcs formed add to 360º.

3. The intercepted arcs of each angle are DOUBLE the measure of the angle.

Intersection #1 - ON the circle

When two 'lines' intersect ON a circle, we see a few important relationships.

1. The angles formed are a linear pair (add to 180º).

2. The two arcs formed add to 360º.

3. The intercepted arcs of each angle are DOUBLE the measure of the angle.

Example

Intersection #2 - Angles formed INSIDE the circle

Intersection #2 - INSIDE the circle

When two 'lines' intersect INSIDE a circle, we have a few important relationships:

1. The angles formed are sets of linear pairs (1 + 2 = 180º).

*Note the vertical angles formed)*

2. All four arcs formed add to 360º.

3. The intercepted arcs on either side of each angle are ADDED, then HALVED.

Intersection #2 - INSIDE the circle

When two 'lines' intersect INSIDE a circle, we have a few important relationships:

1. The angles formed are sets of linear pairs (1 + 2 = 180º).

*Note the vertical angles formed)*

2. All four arcs formed add to 360º.

3. The intercepted arcs on either side of each angle are ADDED, then HALVED.

Intersection #2 - INSIDE the circle

When two 'lines' intersect INSIDE a circle, we have a few important relationships:

1. The angles formed are sets of linear pairs (1 + 2 = 180º).

*Note the vertical angles formed)*

2. All four arcs formed add to 360º.

3. The intercepted arcs on either side of each angle are ADDED, then HALVED.

Example

Finding Segment Lengths of Intersecting Chords

That's it for now!

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