# Unit 8 – Day 1 Homework Assignment - PowerPoint PPT Presentation

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Unit 8 – Day 1 Homework Assignment. Read through and take notes from the following slides Write down any questions you have while reading Things you don ’ t understand Definitions that sound confusing etc Write down and attempt to solve each example problem Leave yourself room to show work.

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Unit 8 – Day 1 Homework Assignment

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### Unit 8 – Day 1 Homework Assignment

• Read through and take notes from the following slides

• Write down any questions you have while reading

• Things you don’t understand

• Definitions that sound confusing

• etc

• Write down and attempt to solve each example problem

• Leave yourself room to show work

### Unit 8 Essential Questions

• What is the difference between tangent, chord and secant lines and how do they relate to segment lengths in a circle?

• How are arc measures related to central, inscribed, and circumscribed angles?

### Unit 8 Bonus Question

• Will be posted on website shortly

### Today’s Objective

11-1 Tangent Lines

• Students will be able to use the relationship between a radius and a tangent.

• Students will be able to use the relationship between two tangents from one point.

### Circle

• Definition:A circle is a set of points equidistant from a given point.

• Name:

• Definition:A segment with one endpoint at the center and one endpoint on the circle.

• Note: All radii of the

same circle are congruent!

### Tangent of a Circle

• Definition: A Tangent Lineis a line that touches a circle at exactly one point.

• Definition: A Point of Tangency is the point where the tangent line touches the circle.

O

B

A

### Theorem 1

• If a line is tangent to a circle, then it is perpendicular to the radius at the point of tangency

O

B

A

### Theorem 2

• Two tangent segments from the same point are congruent

M

L

N

### Example 1 – Find x

• Assume that lines that appear to be tangent are tangent

15

x

12

### Example 2 – Find x

• Assume that lines that appear to be tangent are tangent

L

O

117°

M

N

### Example 3 – Find x

• Assume that lines that appear to be tangent are tangent

H

16

x

I

8

G

### Example 4 – Find MN

• Assume that lines that appear to be tangent are tangent

P

O

35

8

14

N

M

### Inscribed vs Circumscribed

• A figure is INscribed in another figure if it is completely INside the other figure.

• The circle is inscribed in the triangle

• A figure is circumscribed about another figure if it completely surrounds the other figure.

• The circle circumscribes the triangle

### Example 5

• The circle is inscribed in ∆ABC. Find the perimeter of ∆ABC

• Hint: Apply Thm 2