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Turkey MO (2nd round)
1993 Turkey MO (2nd round)
2
turkey 1993 q2
turkey 1993 q2
Source:
October 27, 2006
geometry
parallelogram
geometry unsolved
Problem Statement
I centered incircle of triangle
A
B
C
ABC
A
BC
(
m
(
B
^
)
=
9
0
∘
)
(m(\hat{B})=90^\circ)
(
m
(
B
^
)
=
9
0
∘
)
touches
[
A
B
]
,
[
B
C
]
,
[
A
C
]
\left[AB\right], \left[BC\right], \left[AC\right]
[
A
B
]
,
[
BC
]
,
[
A
C
]
respectively at
F
,
D
,
E
F, D, E
F
,
D
,
E
.
[
C
I
]
∩
[
E
F
]
=
L
\left[CI\right]\cap\left[EF\right]={L}
[
C
I
]
∩
[
EF
]
=
L
and
[
D
L
]
∩
[
A
B
]
=
N
\left[DL\right]\cap\left[AB\right]=N
[
D
L
]
∩
[
A
B
]
=
N
. Prove that
[
A
I
]
=
[
N
D
]
\left[AI\right]=\left[ND\right]
[
A
I
]
=
[
N
D
]
.
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