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Junior Balkan MO
1997 Junior Balkan MO
3
3
Part of
1997 Junior Balkan MO
Problems
(1)
Is that related with Erdosh Mordelli's theorem?
Source: JBMO 1997, Problem 3
6/11/2004
Let
A
B
C
ABC
A
BC
be a triangle and let
I
I
I
be the incenter. Let
N
N
N
,
M
M
M
be the midpoints of the sides
A
B
AB
A
B
and
C
A
CA
C
A
respectively. The lines
B
I
BI
B
I
and
C
I
CI
C
I
meet
M
N
MN
MN
at
K
K
K
and
L
L
L
respectively. Prove that
A
I
+
B
I
+
C
I
>
B
C
+
K
L
AI+BI+CI>BC+KL
A
I
+
B
I
+
C
I
>
BC
+
K
L
. Greece
inequalities