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.

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Unit 8 – Day 1 Homework Assignment

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Unit 8 day 1 homework assignment

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

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

Unit 8 Bonus Question

  • Will be posted on website shortly


Today s objective

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

Circle

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

  • Name:


Radius

Radius

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

  • Note: All radii of the

    same circle are congruent!

(Plural of Radius)


Tangent of a circle

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

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

Theorem 2

  • Two tangent segments from the same point are congruent

M

L

N


Example 1 find x

Example 1 – Find x

  • Assume that lines that appear to be tangent are tangent

15

x

12


Example 2 find x

Example 2 – Find x

  • Assume that lines that appear to be tangent are tangent

L

O

117°

M

N


Example 3 find x

Example 3 – Find x

  • Assume that lines that appear to be tangent are tangent

H

16

x

I

8

G


Example 4 find mn

Example 4 – Find MN

  • Assume that lines that appear to be tangent are tangent

P

O

35

8

14

N

M


Inscribed vs circumscribed

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

Example 5

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

    • Hint: Apply Thm 2


Don t forget to bring your questions

Don’t Forget to Bring your Questions!


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