12.1 circles and tangents
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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. - PowerPoint PPT PresentationTRANSCRIPT
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