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12.1 Circles and Tangents

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 30 min Chapter 12.1 Circles and Tangents.

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12.1 Circles and Tangents

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  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 • 30 min • Chapter 12.1 • Circles and Tangents

  4. 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

  5. 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

  6. 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

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

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

  9. 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.

  10. 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.

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

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

  13. 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.

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

  15. 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.

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

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

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

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