Unit 8 – Day 1 Homework Assignment

1. 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

2. 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?

3. Unit 8 Bonus Question • Will be posted on website shortly

4. 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.

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

6. 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)

7. 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

8. 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

9. Theorem 2 • Two tangent segments from the same point are congruent M L N

10. Example 1 – Find x • Assume that lines that appear to be tangent are tangent 15 x 12

11. Example 2 – Find x • Assume that lines that appear to be tangent are tangent L O 117° M x° N

12. Example 3 – Find x • Assume that lines that appear to be tangent are tangent H 16 x I 8 G

13. Example 4 – Find MN • Assume that lines that appear to be tangent are tangent P O 35 8 14 N M

14. 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

15. Example 5 • The circle is inscribed in ∆ABC. Find the perimeter of ∆ABC • Hint: Apply Thm 2

16. Don’t Forget to Bring your Questions!