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Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2000 National Olympiad First Round
9
9
Part of
2000 National Olympiad First Round
Problems
(1)
Turkey NMO 2000 1st Round - P09 (Geometry)
Source:
7/24/2012
A
B
C
D
E
ABCDE
A
BC
D
E
is convex pentagon.
m
(
B
^
)
=
m
(
D
^
)
=
9
0
∘
m(\widehat{B})=m(\widehat{D})=90^\circ
m
(
B
)
=
m
(
D
)
=
9
0
∘
,
m
(
C
^
)
=
12
0
∘
m(\widehat{C})=120^\circ
m
(
C
)
=
12
0
∘
,
∣
A
B
∣
=
2
|AB|=2
∣
A
B
∣
=
2
,
∣
B
C
∣
=
∣
C
D
∣
=
3
|BC|=|CD|=\sqrt3
∣
BC
∣
=
∣
C
D
∣
=
3
, and
∣
E
D
∣
=
1
|ED|=1
∣
E
D
∣
=
1
.
∣
A
E
∣
=
?
|AE|=?
∣
A
E
∣
=
?
<
s
p
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c
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a
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s
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′
l
a
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′
>
(
A
)
<
/
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p
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>
3
3
2
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p
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=
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(
B
)
<
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2
3
3
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(
C
)
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>
3
2
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=
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x
−
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′
>
(
D
)
<
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>
3
−
1
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−
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d
′
>
(
E
)
<
/
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>
3
<span class='latex-bold'>(A)</span>\ \frac{3\sqrt3}{2} \qquad<span class='latex-bold'>(B)</span>\ \frac{2\sqrt3}{3} \qquad<span class='latex-bold'>(C)</span>\ \frac{3}{2} \qquad<span class='latex-bold'>(D)</span>\ \sqrt3 - 1 \qquad<span class='latex-bold'>(E)</span>\ \sqrt3
<
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A
)
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>
2
3
3
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p
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ss
=
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−
b
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l
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′
>
(
B
)
<
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an
>
3
2
3
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s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
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l
d
′
>
(
C
)
<
/
s
p
an
>
2
3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
3
−
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
3
geometry
trapezoid