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Iran MO (2nd Round)
2004 Iran MO (2nd round)
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Part of
2004 Iran MO (2nd round)
Problems
(1)
AD/DI_a - Iran NMO 2004 (Second Round) - Problem1
Source:
9/24/2010
A
B
C
ABC
A
BC
is a triangle and
∠
A
=
9
0
∘
\angle A=90^{\circ}
∠
A
=
9
0
∘
. Let
D
D
D
be the meet point of the interior bisector of
∠
A
\angle A
∠
A
and
B
C
BC
BC
. And let
I
a
I_a
I
a
be the
A
−
A-
A
−
excenter of
△
A
B
C
\triangle ABC
△
A
BC
. Prove that:
A
D
D
I
a
≤
2
−
1.
\frac{AD}{DI_a}\leq\sqrt{2}-1.
D
I
a
A
D
≤
2
−
1.
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