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Turkey Contests
National Olympiad First Round
2002 National Olympiad First Round
1
1
Part of
2002 National Olympiad First Round
Problems
(1)
P01 [Geometry] - Turkish NMO 1st Round - 2002
Source:
8/7/2014
Let
C
′
,
A
′
,
B
′
C', A', B'
C
′
,
A
′
,
B
′
be the midpoints of sides
[
A
B
]
[AB]
[
A
B
]
,
[
B
C
]
[BC]
[
BC
]
,
[
C
A
]
[CA]
[
C
A
]
of
△
A
B
C
\triangle ABC
△
A
BC
, respectively. Let
H
H
H
be the foot of perpendicular from
A
A
A
to
B
C
BC
BC
. If
∣
A
′
C
′
∣
=
6
|A'C'| = 6
∣
A
′
C
′
∣
=
6
, what is
∣
B
′
H
∣
|B'H|
∣
B
′
H
∣
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
a
)
<
/
s
p
a
n
>
5
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
b
)
<
/
s
p
a
n
>
6
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
c
)
<
/
s
p
a
n
>
5
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
d
)
<
/
s
p
a
n
>
6
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
e
)
<
/
s
p
a
n
>
7
<span class='latex-bold'>a)</span>\ 5 \qquad<span class='latex-bold'>b)</span>\ 6 \qquad<span class='latex-bold'>c)</span>\ 5\sqrt 2 \qquad<span class='latex-bold'>d)</span>\ 6\sqrt 2 \qquad<span class='latex-bold'>e)</span>\ 7
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
a
)
<
/
s
p
an
>
5
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
b
)
<
/
s
p
an
>
6
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
c
)
<
/
s
p
an
>
5
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
d
)
<
/
s
p
an
>
6
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
e
)
<
/
s
p
an
>
7
geometry