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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2000 National Olympiad First Round
25
25
Part of
2000 National Olympiad First Round
Problems
(1)
Turkey NMO 2000 1st Round - P25 (Geometry)
Source:
7/25/2012
The area of a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
is
18
18
18
. If
∣
A
B
∣
+
∣
B
D
∣
+
∣
D
C
∣
=
12
|AB|+|BD|+|DC|=12
∣
A
B
∣
+
∣
B
D
∣
+
∣
D
C
∣
=
12
, then what is
∣
A
C
∣
|AC|
∣
A
C
∣
?
<
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>
(
A
)
<
/
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>
9
<
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>
(
B
)
<
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6
3
<
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>
(
C
)
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8
<
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a
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=
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>
(
D
)
<
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>
6
<
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>
(
E
)
<
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6
2
<span class='latex-bold'>(A)</span>\ 9 \qquad<span class='latex-bold'>(B)</span>\ 6\sqrt 3 \qquad<span class='latex-bold'>(C)</span>\ 8 \qquad<span class='latex-bold'>(D)</span>\ 6 \qquad<span class='latex-bold'>(E)</span>\ 6\sqrt 2
<
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(
A
)
<
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>
9
<
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=
′
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a
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x
−
b
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d
′
>
(
B
)
<
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>
6
3
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=
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x
−
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d
′
>
(
C
)
<
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>
8
<
s
p
an
c
l
a
ss
=
′
l
a
t
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x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
6
<
s
p
an
c
l
a
ss
=
′
l
a
t
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x
−
b
o
l
d
′
>
(
E
)
<
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>
6
2
geometry