10.1– Use Properties of Tangents of Circles. TermDefinitionPicture Circle The set of all points in...
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Transcript of 10.1– Use Properties of Tangents of Circles. TermDefinitionPicture Circle The set of all points in...
![Page 1: 10.1– Use Properties of Tangents of Circles. TermDefinitionPicture Circle The set of all points in a plane that are equidistant from a given point.](https://reader031.fdocuments.in/reader031/viewer/2022020308/56649e995503460f94b9be13/html5/thumbnails/1.jpg)
10.1– Use Properties of Tangents of Circles
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Term Definition Picture
Circle
The set of all points in a plane that are equidistant from a given point
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Term Definition Picture
Center
Point equidistant from the sides of the circle. Gives the name of the circle.
P
P
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Term Definition Picture
Radius
A segment with endpoints at the center and on the circle P
PQ
Q
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Term Definition Picture
Chord
A segment with both endpoints on the circle
P
AQ
QA
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Term Definition Picture
Diameter
A segment with both endpoints on the circle that goes through the center of the circle
P
QR
Q
R
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Term Definition Picture
Secant
A line that intersects a circle in two points.
P
QR�������������� �
Q
R
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Term Definition Picture
Tangent
A line that intersects a circle in exactly one point.
P
QR�������������� �
QR
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Term Definition Picture
Point of Tangency
The point where a tangent line touches a circle
P
QR S
S
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Term Definition Picture
Common Internal Tangent
A line that is tangent inside two circles.
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Term Definition Picture
Common External Tangent
A line that is tangent outside two circles.
![Page 12: 10.1– Use Properties of Tangents of Circles. TermDefinitionPicture Circle The set of all points in a plane that are equidistant from a given point.](https://reader031.fdocuments.in/reader031/viewer/2022020308/56649e995503460f94b9be13/html5/thumbnails/12.jpg)
Term Definition Picture
Coplanar Circles
Two circles on the same plane
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Term Definition Picture
Concentric circles
Circles that have the same center
![Page 14: 10.1– Use Properties of Tangents of Circles. TermDefinitionPicture Circle The set of all points in a plane that are equidistant from a given point.](https://reader031.fdocuments.in/reader031/viewer/2022020308/56649e995503460f94b9be13/html5/thumbnails/14.jpg)
In a plane, a line is ______________ to a circle if and only if the line is ____________________ to a radius of the circle and its endpoint on the circle.
tangentperpendicular
![Page 15: 10.1– Use Properties of Tangents of Circles. TermDefinitionPicture Circle The set of all points in a plane that are equidistant from a given point.](https://reader031.fdocuments.in/reader031/viewer/2022020308/56649e995503460f94b9be13/html5/thumbnails/15.jpg)
Tangent segments from a common ____________ point are ___________________.external congruent
A
B
C
AC AB
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1. State the best term for the given figure.
C
center
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1. State the best term for the given figure.
Common internal tangent
FE�������������� �
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1. State the best term for the given figure.
radius
HG
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1. State the best term for the given figure.
chord
DB
![Page 20: 10.1– Use Properties of Tangents of Circles. TermDefinitionPicture Circle The set of all points in a plane that are equidistant from a given point.](https://reader031.fdocuments.in/reader031/viewer/2022020308/56649e995503460f94b9be13/html5/thumbnails/20.jpg)
1. State the best term for the given figure.
Point of Tangency
F
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1. State the best term for the given figure.
diameter
BE
![Page 22: 10.1– Use Properties of Tangents of Circles. TermDefinitionPicture Circle The set of all points in a plane that are equidistant from a given point.](https://reader031.fdocuments.in/reader031/viewer/2022020308/56649e995503460f94b9be13/html5/thumbnails/22.jpg)
1. State the best term for the given figure.
secant
DB�������������� �
![Page 23: 10.1– Use Properties of Tangents of Circles. TermDefinitionPicture Circle The set of all points in a plane that are equidistant from a given point.](https://reader031.fdocuments.in/reader031/viewer/2022020308/56649e995503460f94b9be13/html5/thumbnails/23.jpg)
1. State the best term for the given figure.
Common External Tangent
AG�������������� �
![Page 24: 10.1– Use Properties of Tangents of Circles. TermDefinitionPicture Circle The set of all points in a plane that are equidistant from a given point.](https://reader031.fdocuments.in/reader031/viewer/2022020308/56649e995503460f94b9be13/html5/thumbnails/24.jpg)
2. Find the radius of .A
2u
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3. Find the diameter of .B
4u
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4. Find the center of .C
(2, 4)
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5. The points K and M are points of tangency. Find the value of x.
x = 22
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5. The points K and M are points of tangency. Find the value of x.
4x + 7 = 7x – 8
7 = 3x – 8
15 = 3x
5 = x
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6. In the diagram, is a radius of Determine whether is tangent to Explain your reasoning.
BC .CAB .C
c2 = a2 + b2
52 = 32 + 42
25 = 9 + 16
25 = 25
Right Triangle
Yes
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c2 = a2 + b2
192 = 82 + 162
361 = 64 + 256
361 > 320
Not a Right Triangle
NO
6. In the diagram, is a radius of Determine whether is tangent to Explain your reasoning.
BC .CAB .C
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7. Given the picture, find the indicated length.
c2 = a2 + b2
802 = a2 + 482
6400 = a2 + 2304
4096 = a2
64a
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Given the picture, find the indicated length.
c2 = a2 + b2
252 = x2 + 122
625 = x2 + 144
481 = x2
481 x
6
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Given the picture, find the indicated length.Given the picture, find the indicated length.
c2 = a2 + b2
(r + 2)2 = r2 + 42
r2 + 4r + 4 = r2 + 16
4r + 4 = 16
4r = 12
r = 3
(r + 2)(r + 2) = r2 + 16
r2 + 2r + 2r + 4 = r2 + 16
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Given the picture, find the indicated length.
c2 = a2 + b2
(r + 9)2 = r2 + 152
r2 + 18r + 81 = r2 + 225
18r + 81 = 225
18r = 144
r = 8
(r + 9)(r + 9) = r2 + 225
r2 + 9r + 9r + 81 = r2 + 225
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c2 = a2 + b2
(r + 16)2 = r2 + 242
r2 + 32r + 256 = r2 + 57632r + 256 = 576
32r = 320r = 10
(r + 16)(r + 16) = r2 + 576r2 + 16r + 16r + 256 = r2 + 576
10.1 655-657 3-10, 15-23 odd, 24, 27, 28
HW Problem
#21