1. 12.1 Circles and Tangents
Brett Solberg AHS ‘11-’12

2. Warm-ups 1) What is the distance between (-1, 4) and (4, -2)?
2) What is the angle measure of x?
3) What is the measure of x?

3. Today’s Agenda Chapter 1 – 5 Review Game Chapter 12.1 30 min
Circles and Tangents

5. Review Game Group 1 – Sharlanae, Brindee, Kevin, Armin, Pouria
Group 2 – Courtney, Wyatt, Brennan, Brett, Camerone
Group 3 – Aubrey, Derek, Logan, Julianne, Lillian
Group 4 – Jesse, Gabby, Becca, Jordan, Jessica,
Group 5 – Lucky, Kaitlyn, Andrea, Amanda, Abbie
Group 6 – Austin, Sebastian, Grayson, Bridger, Hayden
Group 7 – Johnny, Kendel, Torrey, Macie
Group 8 – Corey, Shea, Abigail, Jeni

6. Review Game Group 1 – Emilie, Chris B, Mason, Jenna, Josi
Group 2 – Hannah, Ivy, Michael, Shelby, Trevor
Group 3 – Mallory, Landen, Chris J, Cody, Dylan
Group 4 – Anthony, Alex N, Andre, Bridger, Brittany
Group 5 – Connor P, Blake, Michaela, Christian
Group 6 – Nikol, Alea, Tryston, Alex T
Group 7 – Connor V, Wyatt, Aaron

7. Review Game Group 1 - Jestine, Kade, Julianne, Karli
Group 2 - Caitlin, Laura, Kylan, Sam, Katie
Group 3 – Connor, Logan, Cassidy, Sierra
Group 4 – Alexandria, Chandler, Mitch, Hunter
Group 5 – Briel, Preston, Kyle, Coleman, Tanner
Group 6 – Kolton, Jacob, Shelby, Victoria
Group 7 - Carsen Sydney Garrett, Kathleen, Tanner C

8. Review Game Each group needs: 1 Whiteboard 1 Marker 1 Eraser
1 Team name
1 Review Sheet

9. Circles How many times can a line intersect a circle? No intersection
2 Intersections
Secant
1 Intersection
Tangent

10. Tangent Lines
A tangent to a circle is a line that intersects a circle at exactly one point.
The point of intersection is called
the point of tangency.

11. Theorem 12-1
If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

12. Example 1
BA is tangent to Circle C at point A. The measure of angle B is 22˚. Find the value of x.

13. Example 2
ML and MN are tangent to circle O. Find the value of x.

14. Theorem 12.2
Converse of 12.1
If a line is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle.

15. Example 3
Is ML tangent to circle N at point L? Explain?

16. Inscribed/Circumscribed
Inscribed Circle – A circle which is tangent to all the sides of a polygon.
Circumscribed Circle – A circle which is tangent to all the vertices of a triangle.

17. Theorem 12.3
2 segments tangent to a circle from a point outside the circle are congruent.

18. Example 4
Circle C is inscribed by XYZW. Find the perimeter of XYZW.

19. Assignment 12.1 Worksheet Due next class
Late assignments worth half credit