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Akdeniz University MO
1997 Akdeniz University MO
5
geometric ineq.
geometric ineq.
Source:
January 30, 2016
geometric inequality
geometry
Problem Statement
A
A
B
C
ABC
A
BC
triangle divide by a
d
d
d
line such that, new two pieces' areas are equal.
d
d
d
line intersects with
[
A
B
]
[AB]
[
A
B
]
at
D
D
D
,
[
A
C
]
[AC]
[
A
C
]
at
E
E
E
. Prove that
A
D
+
A
E
B
D
+
D
E
+
E
C
+
C
B
>
1
4
\frac{AD+AE}{BD+DE+EC+CB} > \frac{1}{4}
B
D
+
D
E
+
EC
+
CB
A
D
+
A
E
>
4
1
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