Secants Through a Circle

4.2a - Intersecting Chords, Secants and Tangents in Circles

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Multiple Choice

Find the measure of the missing inscribed angle, x.

• 30º

• 60º

• 120º

• 15º

More Circle Vocabulary

*You will not have to identify chords, secants, or tangents directly.*

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

Multiple Choice

Find the measure of the missing angle.

• 40º

• 80º

• 160º

• 100º

Multiple Choice

Find the measure of the missing angle.

• 65º

• 115º

• 360º

• 180º

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

Poll

Which one best describes you for 4.2a?

• I am confident in my ability to learn this topic.

• I am unsure about my ability to learn this topic.

• I am not optimistic about my ability to learn this topic.

That's it for now!

There is one more intersection type that we will look at next class!!

4.2b next class (1/12-13)

4.2 Review (1/14-15)

Module 4 Summative (1/19-20)