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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2001 National Olympiad First Round
5
5
Part of
2001 National Olympiad First Round
Problems
(1)
P05 [Geometry] - Turkish NMO 1st Round - 2001
Source:
4/18/2014
Let
A
B
C
D
ABCD
A
BC
D
be a trapezoid such that
A
B
∥
C
D
AB \parallel CD
A
B
∥
C
D
,
∣
A
B
∣
<
∣
C
D
∣
|AB|<|CD|
∣
A
B
∣
<
∣
C
D
∣
, and
Area
(
A
B
C
)
=
30
\text{Area}(ABC)=30
Area
(
A
BC
)
=
30
. Let the line through
B
B
B
parallel to
A
D
AD
A
D
meet
[
A
C
]
[AC]
[
A
C
]
at
E
E
E
. If
∣
A
E
∣
:
∣
E
C
∣
=
3
:
2
|AE|:|EC|=3:2
∣
A
E
∣
:
∣
EC
∣
=
3
:
2
, then what is the area of trapezoid
A
B
C
D
ABCD
A
BC
D
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
45
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
60
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
72
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
80
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
90
<span class='latex-bold'>(A)</span>\ 45 \qquad<span class='latex-bold'>(B)</span>\ 60 \qquad<span class='latex-bold'>(C)</span>\ 72 \qquad<span class='latex-bold'>(D)</span>\ 80 \qquad<span class='latex-bold'>(E)</span>\ 90
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
45
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
60
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
72
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
80
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
90
geometry
trapezoid