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

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Presentation transcript:

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

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?

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

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

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

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

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

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

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.

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.

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

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

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.

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

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.

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

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

Assignment 12.1 Worksheet Due next class Late assignments worth half credit