Chords, Tangents, & Secants

Intersecting Chords, Secants and Tangents in Circles

Dr. Tom Giles

Multiple Choice

• 33

• 18

• 46

• 16

Multiple Choice

Find the measure of the missing inscribed angle, x.

• 30º

• 60º

• 120º

• 15º

Multiple Choice

• 240
• 230
• 205
• 255

More Circle Vocabulary

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

Multiple Choice

Find the value of x.

• 10
• 181
• 34
• 40

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

and the 3 different formulas associated with them.

Multiple Choice

Find the value of x.

• 12.5
• 8
• 35
• 16

Intersection #1 - Angle formed ON the circle

Multiple Choice

Find the radius r

• 2
• 3
• 4
• 5

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.

Multiple Choice

Find the measure of ∠ABE.

• 129⁰

• 51⁰

• 100⁰

• 65⁰

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.

Multiple Choice

In the diagram, TP and TQ are tangents to circle O. Determine the value of x. (Note the angles with single arcs are not necessarily congruent in this diagram.)

• 70

• 110

• 140

• 90

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.

Multiple Choice

Find the perimeter of the triangle.

• A
• B
• C
• D

Example

Multiple Choice

Find x

• 10
• 5
• 18
• 9

Multiple Choice

Find the measure of the missing angle.

• 40º

• 80º

• 160º

• 100º

Multiple Choice

Given the following inscribed quadrilateral, what is the value of y?

• 10
• 20
• 30
• 40

Multiple Choice

Find the measure of the missing angle.

• 65º

• 115º

• 360º

• 180º

Multiple Choice

x = ?

• 90
• 180
• 45
• 80

Intersection #2 - Angles formed INSIDE the circle

Multiple Choice

Find x.  Assume that segments that appear to be   tangent are tangent.

• 2
• 11
• 7.6
• 9

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.

Multiple Choice

What is the measure of angle 2?

• 80
• 45
• 125
• 40

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.

Multiple Choice

Solve for x.

• 29
• 33
• 41.5
• 50

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.

Multiple Choice

Find the measure of the missing arc.

• 70°

• 100.5°

• 201°

• 140°

Example