Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You...
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![Page 1: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/1.jpg)
Warm UpDirections: Create your own definition for as many of
the vocabulary words listed below. You may use diagrams in your explanations.
circle radius diameter
radii chord secant
tangent concentric circles
common tangent point of tangency
![Page 2: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/2.jpg)
![Page 3: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/3.jpg)
Using a compass…Construct a circle, remember to label the
center of the circle before drawing your circle. Label the circle Q.
Then, using a straightedge, draw a line tangent to the circle. Label this line l.
Connect a radius from the center to the point of tangency. Label this point P.
What do you notice?
![Page 4: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/4.jpg)
Theorem 10.1 If a line is tangent to a circle, then it is
perpendicular to the radius drawn to the point of tangency.
If l is tangent to ⨀Q at P, then l .
€
PQ
![Page 5: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/5.jpg)
Theorem 10.2In a plane, if a line is perpendicular to a
radius of a circle at its endpoint on the circle, then the line is tangent to the circle.
If l at P, then l is tangent to ⨀Q.
€
PQ
![Page 6: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/6.jpg)
Theorem 10.3If two segments from the same exterior
point are tangent to a circle, then they are congruent.
⨀
€
If SR and ST are tangent to P, then SR ≅ ST.
![Page 7: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/7.jpg)
Tell whether the line or segment is best described as a chord, a secant, a tangent, a diameter, or a radius of C.⨀
A diameter is a chord but not all chords are diameters
![Page 8: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/8.jpg)
Common tangent: A line or segment that is tangent to two coplanar circles A common internal
tangent intersects the segment that joins the centers of the two circles.
A common external tangent does not intersect the segment that joins the centers of the two circles.
![Page 9: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/9.jpg)
How many common tangents are there?
4 common tangents: 2 external and 2 internal
3 common tangents: 2 external and 1 internal
![Page 10: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/10.jpg)
How many common tangents are there?
2 common tangents: 2 external and 0 internal
1 common tangents: 1 external and 0 internal
![Page 11: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/11.jpg)
How many common tangents are there?
0 common tangent
0 common tangent
![Page 12: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/12.jpg)
Segment AB is tangent to C at B. Segment AD ⨀is tangent to C at D. Find the value of x. ⨀
€
x 2 − 4 = 21
€
x 2 = 25
x = 25
x = ±5
![Page 13: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/13.jpg)
You are standing at C, 14 feet from a water tower. The distance from you to a point of tangency on the tower is 28 feet. What is the radius of the water tower?
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r2 + 282 = (r +14)2
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r2 + 784 = r2 + 28r +196
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784 = 28r +196
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588 = 28r
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21 = r
![Page 14: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/14.jpg)
Is segment CE tangent to D? ⨀Explain.
![Page 15: Warm Up Directions: Create your own definition for as many of the vocabulary words listed below. You may use diagrams in your explanations. circle radiusdiameter.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649eb65503460f94bbf614/html5/thumbnails/15.jpg)
Find the values of x, y, and z in the diagram.