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Proof of Tangency
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Expression 35: "N" Subscript, 1 , Baseline equals "C" Subscript, 1 , Baseline plus StartFraction, "C" Subscript, "N" , Baseline Over "A" Subscript, "C" , Baseline , EndFraction left parenthesis, "B" Subscript, 1 , Baseline minus "C" Subscript, 1 , Baseline , right parenthesis
N
1
=
C
1
+
C
N
A
C
B
1
−
C
1
equals
=
3.7 2 7 9 2 2 0 6 1 3 6
3
.
7
2
7
9
2
2
0
6
1
3
6
35
Expression 36: "N" Subscript, 2 , Baseline equals "C" Subscript, 2 , Baseline plus StartFraction, "C" Subscript, "N" , Baseline Over "A" Subscript, "C" , Baseline , EndFraction left parenthesis, negative "C" Subscript, 2 , Baseline , right parenthesis
N
2
=
C
2
+
C
N
A
C
−
C
2
equals
=
5.2 7 2 0 7 7 9 3 8 6 4
5
.
2
7
2
0
7
7
9
3
8
6
4
36
Expression 37: "P" Subscript, 1 , Baseline equals StartFraction, "B" Subscript, 1 , Baseline plus "C" Subscript, 1 , Baseline Over 2 , EndFraction
P
1
=
B
1
+
C
1
2
equals
=
4.5
4
.
5
37
Expression 38: "P" Subscript, 2 , Baseline equals StartFraction, "B" Subscript, 2 , Baseline plus "C" Subscript, 2 , Baseline Over 2 , EndFraction
P
2
=
B
2
+
C
2
2
equals
=
4.5
4
.
5
38
Expression 39: "T" Subscript, 1 , Baseline equals "P" Subscript, 1 , Baseline plus StartFraction, "R" Subscript, 2 , Baseline plus distance left parenthesis, "M" , "P" , right parenthesis Over distance left parenthesis, "M" , "P" , right parenthesis , EndFraction left parenthesis, "M" Subscript, 1 , Baseline minus "P" Subscript, 1 , Baseline , right parenthesis
T
1
=
P
1
+
R
2
+
d
i
s
t
a
n
c
e
M
,
P
d
i
s
t
a
n
c
e
M
,
P
M
1
−
P
1
equals
=
negative 1.2 4 2 6 4 0 6 8 7 1 2
−
1
.
2
4
2
6
4
0
6
8
7
1
2
39
Expression 40: "T" Subscript, 2 , Baseline equals "P" Subscript, 2 , Baseline plus StartFraction, "R" Subscript, 2 , Baseline plus distance left parenthesis, "M" , "P" , right parenthesis Over distance left parenthesis, "M" , "P" , right parenthesis , EndFraction left parenthesis, "M" Subscript, 2 , Baseline minus "P" Subscript, 2 , Baseline , right parenthesis
T
2
=
P
2
+
R
2
+
d
i
s
t
a
n
c
e
M
,
P
d
i
s
t
a
n
c
e
M
,
P
M
2
−
P
2
equals
=
1.7 5 7 3 5 9 3 1 2 8 8
1
.
7
5
7
3
5
9
3
1
2
8
8
40
Graphs
Graphs
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41
Expression 42: "y" less than 20
y
<
2
0
42
Expression 43: left parenthesis, "L" Subscript, 1 , Baseline plus "R" Subscript, 1 , Baseline cos "t" , "L" Subscript, 2 , Baseline plus "R" Subscript, 1 , Baseline sin "t" , right parenthesis
L
1
+
R
1
c
o
s
t
,
L
2
+
R
1
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 360
3
6
0
43
Expression 44: left parenthesis, "L" Subscript, 1 , Baseline plus "R" Subscript, 1 , Baseline cos "t" , "L" Subscript, 2 , Baseline plus "R" Subscript, 1 , Baseline sin "t" , right parenthesis
L
1
+
R
1
c
o
s
t
,
L
2
+
R
1
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 360
3
6
0
44
Expression 45: left parenthesis, "M" Subscript, 1 , Baseline plus "R" Subscript, 2 , Baseline cos "t" , "M" Subscript, 2 , Baseline plus "R" Subscript, 2 , Baseline sin "t" , right parenthesis
M
1
+
R
2
c
o
s
t
,
M
2
+
R
2
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 360
3
6
0
45
Expression 46: left parenthesis, "M" Subscript, 1 , Baseline plus "R" Subscript, 2 , Baseline cos "t" , "M" Subscript, 2 , Baseline plus "R" Subscript, 2 , Baseline sin "t" , right parenthesis
M
1
+
R
2
c
o
s
t
,
M
2
+
R
2
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 360
3
6
0
46
Expression 47: polygon left parenthesis, "P" , "T" , right parenthesis
p
o
l
y
g
o
n
P
,
T
47
Expression 48: polygon left parenthesis, "A" , "C" , right parenthesis
p
o
l
y
g
o
n
A
,
C
48
Expression 49: polygon left parenthesis, "B" , "C" , right parenthesis
p
o
l
y
g
o
n
B
,
C
49
Expression 50: polygon left parenthesis, "A" , "N" , right parenthesis
p
o
l
y
g
o
n
A
,
N
50
Expression 51: left parenthesis, "R" cos "t" , "R" sin "t" , right parenthesis
R
c
o
s
t
,
R
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 180
1
8
0
51
Expression 52: left parenthesis, "R" cos "t" , "R" sin 0 , right parenthesis
R
c
o
s
t
,
R
s
i
n
0
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 180
1
8
0
52
Expression 53: left parenthesis, "L" Subscript, 1 , Baseline plus "R" Subscript, 1 , Baseline cos "t" , "L" Subscript, 2 , Baseline plus "R" Subscript, 1 , Baseline sin "t" , right parenthesis
L
1
+
R
1
c
o
s
t
,
L
2
+
R
1
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 360
3
6
0
53
Expression 54: left parenthesis, "P" Subscript, 1 , Baseline plus "R" Subscript, 3 , Baseline cos "t" , "P" Subscript, 2 , Baseline plus "R" Subscript, 3 , Baseline sin "t" , right parenthesis
P
1
+
R
3
c
o
s
t
,
P
2
+
R
3
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 360
3
6
0
54
Expression 55: left parenthesis, "M" Subscript, 1 , Baseline plus "R" Subscript, 2 , Baseline cos "t" , "M" Subscript, 2 , Baseline plus "R" Subscript, 2 , Baseline sin "t" , right parenthesis
M
1
+
R
2
c
o
s
t
,
M
2
+
R
2
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 360
3
6
0
55
Points
Points
Hide this folder from students.
56
NEW.JPG
NEW.JPG
Change Image
Center:
center: left parenthesis, negative 7.0 9 , 9.8 8 , right parenthesis
−
7
.
0
9
,
9
.
8
8
Width:
width: 6.0 9 7
6
.
0
9
7
Angle:
angle: 0
0
Height:
height: 3.2 2 8
3
.
2
2
8
Opacity:
opacity: 1
1
57
O: "O" equals left parenthesis, "O" Subscript, 1 , Baseline , "O" Subscript, 2 , Baseline , right parenthesis
O
=
O
1
,
O
2
Label:
equals
=
left parenthesis, 0 , 0 , right parenthesis
0
,
0
58
P: "P" equals left parenthesis, "P" Subscript, 1 , Baseline , "P" Subscript, 2 , Baseline , right parenthesis
P
=
P
1
,
P
2
Label:
equals
=
left parenthesis, 4.5 , 4.5 , right parenthesis
4
.
5
,
4
.
5
59
A: "A" equals left parenthesis, "A" Subscript, 1 , Baseline , "A" Subscript, 2 , Baseline , right parenthesis
A
=
A
1
,
A
2
Label:
equals
=
left parenthesis, negative 9 , 0 , right parenthesis
−
9
,
0
60
B: "B" equals left parenthesis, "B" Subscript, 1 , Baseline , "B" Subscript, 2 , Baseline , right parenthesis
B
=
B
1
,
B
2
Label:
equals
=
left parenthesis, 9 , 0 , right parenthesis
9
,
0
61
C: "C" equals left parenthesis, "C" Subscript, 1 , Baseline , "C" Subscript, 2 , Baseline , right parenthesis
C
=
C
1
,
C
2
Label:
equals
=
left parenthesis, 0 , 9 , right parenthesis
0
,
9
62
L: "L" equals left parenthesis, "L" Subscript, 1 , Baseline , "L" Subscript, 2 , Baseline , right parenthesis
L
=
L
1
,
L
2
Label:
equals
=
left parenthesis, negative 3.6 7 5 5 0 2 1 3 , 2.2 0 5 4 7 9 2 3 , right parenthesis
−
3
.
6
7
5
5
0
2
1
3
,
2
.
2
0
5
4
7
9
2
3
63
M: "M" equals left parenthesis, "M" Subscript, 1 , Baseline , "M" Subscript, 2 , Baseline , right parenthesis
M
=
M
1
,
M
2
Label:
equals
=
left parenthesis, 1.5 4 4 1 5 5 8 8 , 3.0 8 8 3 1 1 7 5 , right parenthesis
1
.
5
4
4
1
5
5
8
8
,
3
.
0
8
8
3
1
1
7
5
64
N: "N" equals left parenthesis, "N" Subscript, 1 , Baseline , "N" Subscript, 2 , Baseline , right parenthesis
N
=
N
1
,
N
2
Label:
equals
=
left parenthesis, 3.7 2 7 9 2 2 0 6 , 5.2 7 2 0 7 7 9 4 , right parenthesis
3
.
7
2
7
9
2
2
0
6
,
5
.
2
7
2
0
7
7
9
4
65
T: "T" equals left parenthesis, "T" Subscript, 1 , Baseline , "T" Subscript, 2 , Baseline , right parenthesis
T
=
T
1
,
T
2
Label:
equals
=
left parenthesis, negative 1.2 4 2 6 4 0 6 9 , 1.7 5 7 3 5 9 3 1 , right parenthesis
−
1
.
2
4
2
6
4
0
6
9
,
1
.
7
5
7
3
5
9
3
1
66
AC = BC: midpoint left parenthesis, "A" , "C" , right parenthesis
m
i
d
p
o
i
n
t
A
,
C
Label:
equals
=
left parenthesis, negative 4.5 , 4.5 , right parenthesis
−
4
.
5
,
4
.
5
67
Hidden Label: left parenthesis, "A" Subscript, 1 , Baseline plus 1.5cos theta Subscript, 1 , Baseline , "A" Subscript, 2 , Baseline plus 1.5sin theta Subscript, 1 , Baseline , right parenthesis
A
1
+
1
.
5
c
o
s
θ
1
,
A
2
+
1
.
5
s
i
n
θ
1
Label
equals
=
left parenthesis, negative 7.5 2 9 , 0.2 9 2 6 , right parenthesis
−
7
.
5
2
9
,
0
.
2
9
2
6
left parenthesis, negative 7.7 5 3 , 0.8 3 3 4 , right parenthesis
−
7
.
7
5
3
,
0
.
8
3
3
4
68
Expression 69: theta Subscript, 1 , Baseline equals left bracket, 45 quarters , StartFraction, 3 times 45 Over 4 , EndFraction , right bracket
θ
1
=
4
5
4
,
3
·
4
5
4
equals
=
11.2 5
1
1
.
2
5
33.7 5
3
3
.
7
5
69
70
powered by
powered by
O
P
A
B
C
L
M
N
T
AC = BC
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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