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Contests
International Contests
Czech-Polish-Slovak Match
1998 Czech and Slovak Match
3
3
Part of
1998 Czech and Slovak Match
Problems
(1)
inequality in a convex hexagon with equal sides in pairs
Source: Czech and Slovak Match 1998 P3
10/1/2017
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
. When does equality occur?
inequalities
convex polygon
hexagon
triangle inequality