12.1 circles and tangents
DESCRIPTION
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
![Page 1: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/1.jpg)
12.1 Circles and Tangents
Brett Solberg AHS ‘11-’12
![Page 2: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/2.jpg)
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?
![Page 3: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/3.jpg)
Today’s Agenda
0Chapter 1 – 5 Review Game0 30 min
0Chapter 12.10 Circles and Tangents
![Page 4: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/4.jpg)
![Page 5: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/5.jpg)
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
![Page 6: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/6.jpg)
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
![Page 7: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/7.jpg)
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
![Page 8: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/8.jpg)
Review Game
0Each group needs:0 1 Whiteboard0 1 Marker0 1 Eraser0 1 Team name0 1 Review Sheet
![Page 9: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/9.jpg)
Circles
0How many times can a line intersect a circle?
0No intersection0 Line
02 Intersections0 Secant
01 Intersection0 Tangent
![Page 10: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/10.jpg)
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.
![Page 11: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/11.jpg)
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.
![Page 12: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/12.jpg)
Example 1
0BA is tangent to Circle C at point A. The measure of angle B is 22˚. Find the value of x.
![Page 13: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/13.jpg)
Example 2
0ML and MN are tangent to circle O. Find the value of x.
![Page 14: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/14.jpg)
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.
![Page 15: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/15.jpg)
Example 3
0 Is ML tangent to circle N at point L? Explain?
![Page 16: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/16.jpg)
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.
![Page 17: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/17.jpg)
Theorem 12.3
02 segments tangent to a circle from a point outside the circle are congruent.
![Page 18: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/18.jpg)
Example 4
0Circle C is inscribed by XYZW. Find the perimeter of XYZW.
![Page 19: 12.1 Circles and Tangents](https://reader036.vdocument.in/reader036/viewer/2022062304/56813bf3550346895da52e2f/html5/thumbnails/19.jpg)
Assignment
012.1 Worksheet0 Due next class0 Late assignments worth half credit