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National and Regional Contests
Turkey Contests
National Olympiad First Round
2010 National Olympiad First Round
9
9
Part of
2010 National Olympiad First Round
Problems
(1)
Turkey NMO 2010 1st Round - P09 (Geometry)
Source:
7/26/2012
Let
E
E
E
be a point outside of square
A
B
C
D
ABCD
A
BC
D
. If the distance of
E
E
E
to
A
C
AC
A
C
is
6
6
6
, to
B
D
BD
B
D
is
17
17
17
, and to the nearest vertex of the square is
10
10
10
, what is the area of the square?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
200
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
196
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
169
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
162
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
144
<span class='latex-bold'>(A)</span>\ 200 \qquad<span class='latex-bold'>(B)</span>\ 196 \qquad<span class='latex-bold'>(C)</span>\ 169 \qquad<span class='latex-bold'>(D)</span>\ 162 \qquad<span class='latex-bold'>(E)</span>\ 144
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
200
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
196
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
169
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
162
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
144
geometry