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Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2013 National Olympiad First Round
5
5
Part of
2013 National Olympiad First Round
Problems
(1)
P05 [Geometry] - Turkish NMO 1st Round - 2013
Source:
4/16/2013
Let
D
D
D
be a point on side
[
B
C
]
[BC]
[
BC
]
of triangle
A
B
C
ABC
A
BC
where
∣
B
C
∣
=
11
|BC|=11
∣
BC
∣
=
11
and
∣
B
D
∣
=
8
|BD|=8
∣
B
D
∣
=
8
. The circle passing through the points
C
C
C
and
D
D
D
touches
A
B
AB
A
B
at
E
E
E
. Let
P
P
P
be a point on the line which is passing through
B
B
B
and is perpendicular to
D
E
DE
D
E
. If
∣
P
E
∣
=
7
|PE|=7
∣
PE
∣
=
7
, then what is
∣
D
P
∣
|DP|
∣
D
P
∣
?
<
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
>
4
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
3
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
None of above
<span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 4 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 2 \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
<
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
>
4
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
None of above
geometry