10.1– use properties of tangents of circles. termdefinitionpicture circle the set of all points in...
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10.1– Use Properties of Tangents of Circles
Term Definition Picture
Circle
The set of all points in a plane that are equidistant from a given point
Term Definition Picture
Center
Point equidistant from the sides of the circle. Gives the name of the circle.
P
P
Term Definition Picture
Radius
A segment with endpoints at the center and on the circle P
PQ
Q
Term Definition Picture
Chord
A segment with both endpoints on the circle
P
AQ
QA
Term Definition Picture
Diameter
A segment with both endpoints on the circle that goes through the center of the circle
P
QR
Q
R
Term Definition Picture
Secant
A line that intersects a circle in two points.
P
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Q
R
Term Definition Picture
Tangent
A line that intersects a circle in exactly one point.
P
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QR
Term Definition Picture
Point of Tangency
The point where a tangent line touches a circle
P
QR S
S
Term Definition Picture
Common Internal Tangent
A line that is tangent inside two circles.
Term Definition Picture
Common External Tangent
A line that is tangent outside two circles.
Term Definition Picture
Coplanar Circles
Two circles on the same plane
Term Definition Picture
Concentric circles
Circles that have the same center
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
Tangent segments from a common ____________ point are ___________________.external congruent
A
B
C
AC AB
1. State the best term for the given figure.
C
center
1. State the best term for the given figure.
Common internal tangent
FE�������������� �
1. State the best term for the given figure.
radius
HG
1. State the best term for the given figure.
chord
DB
1. State the best term for the given figure.
Point of Tangency
F
1. State the best term for the given figure.
diameter
BE
1. State the best term for the given figure.
secant
DB�������������� �
1. State the best term for the given figure.
Common External Tangent
AG�������������� �
2. Find the radius of .A
2u
3. Find the diameter of .B
4u
4. Find the center of .C
(2, 4)
5. The points K and M are points of tangency. Find the value of x.
x = 22
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
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
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
7. Given the picture, find the indicated length.
c2 = a2 + b2
802 = a2 + 482
6400 = a2 + 2304
4096 = a2
64a
Given the picture, find the indicated length.
c2 = a2 + b2
252 = x2 + 122
625 = x2 + 144
481 = x2
481 x
6
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
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
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