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National and Regional Contests
Iran Contests
Iran MO (3rd Round)
1998 Iran MO (3rd Round)
2
Convex Hexagon
Convex Hexagon
Source: Iran Third Round MO 1998, Exam 4, P2
October 31, 2010
inequalities
geometry unsolved
geometry
Problem Statement
Let
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
be a convex hexagon such that
A
B
=
B
C
,
C
D
=
D
E
AB = BC, CD = DE
A
B
=
BC
,
C
D
=
D
E
and
E
F
=
F
A
EF = FA
EF
=
F
A
. Prove that
A
B
B
E
+
C
D
A
D
+
E
F
C
F
≥
3
2
.
\frac{AB}{BE}+\frac{CD}{AD}+\frac{EF}{CF} \geq \frac{3}{2}.
BE
A
B
+
A
D
C
D
+
CF
EF
≥
2
3
.
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