12.1 Circles and Tangents

Brett Solberg AHS ‘11-’12

Warm-ups

01) What is the distance between (-1, 4) and (4, -2)?

02) What is the angle measure of x?

03) What is the measure of x?

Today’s Agenda

0Chapter 1 – 5 Review Game0 30 min

0Chapter 12.10 Circles and Tangents

Review Game

0Group 1 – Sharlanae, Brindee, Kevin, Armin, Pouria0Group 2 – Courtney, Wyatt, Brennan, Brett, Camerone0Group 3 – Aubrey, Derek, Logan, Julianne, Lillian0Group 4 – Jesse, Gabby, Becca, Jordan, Jessica, 0Group 5 – Lucky, Kaitlyn, Andrea, Amanda, Abbie0Group 6 – Austin, Sebastian, Grayson, Bridger, Hayden0Group 7 – Johnny, Kendel, Torrey, Macie0Group 8 – Corey, Shea, Abigail, Jeni

Review Game

0Group 1 – Emilie, Chris B, Mason, Jenna, Josi0Group 2 – Hannah, Ivy, Michael, Shelby, Trevor0Group 3 – Mallory, Landen, Chris J, Cody, Dylan0Group 4 – Anthony, Alex N, Andre, Bridger, Brittany0Group 5 – Connor P, Blake, Michaela, Christian0Group 6 – Nikol, Alea, Tryston, Alex T0Group 7 – Connor V, Wyatt, Aaron

Review Game

0Group 1 - Jestine, Kade, Julianne, Karli0Group 2 - Caitlin, Laura, Kylan, Sam, Katie0Group 3 – Connor, Logan, Cassidy, Sierra0Group 4 – Alexandria, Chandler, Mitch, Hunter0Group 5 – Briel, Preston, Kyle, Coleman, Tanner0Group 6 – Kolton, Jacob, Shelby, Victoria0Group 7 - Carsen Sydney Garrett, Kathleen, Tanner C

Review Game

0Each group needs:0 1 Whiteboard0 1 Marker0 1 Eraser0 1 Team name0 1 Review Sheet

Circles

0How many times can a line intersect a circle?

0No intersection0 Line

02 Intersections0 Secant

01 Intersection0 Tangent

Tangent Lines

0A tangent to a circle is a line that intersects a circle at exactly one point.

0The point of intersection is called the point of tangency.

Theorem 12-1

0 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

Example 1

0BA is tangent to Circle C at point A. The measure of angle B is 22˚. Find the value of x.

Example 2

0ML and MN are tangent to circle O. Find the value of x.

Theorem 12.2

0Converse of 12.10 If a line is perpendicular to a radius at its endpoint on

the circle, then the line is tangent to the circle.

Example 3

0 Is ML tangent to circle N at point L? Explain?

Inscribed/Circumscribed

0 Inscribed Circle – A circle which is tangent to all the sides of a polygon.

0Circumscribed Circle – A circle which is tangent to all the vertices of a triangle.

Theorem 12.3

02 segments tangent to a circle from a point outside the circle are congruent.

Example 4

0Circle C is inscribed by XYZW. Find the perimeter of XYZW.

Assignment

012.1 Worksheet0 Due next class0 Late assignments worth half credit