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Korea National Olympiad
1997 Korea National Olympiad
3
Ineq in Geo
Ineq in Geo
Source: 1997 Korea National Olympiad #3
March 18, 2018
inequalities
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
,
E
F
=
F
A
.
AB=BC,CD=DE, EF=FA.
A
B
=
BC
,
C
D
=
D
E
,
EF
=
F
A
.
Prove that
B
C
B
E
+
D
E
D
A
+
F
A
F
C
≥
3
2
\frac{BC}{BE}+\frac{DE}{DA}+\frac{FA}{FC}\ge\frac{3}{2}
BE
BC
+
D
A
D
E
+
FC
F
A
≥
2
3
and find when equality holds.
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