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Tournament Of Towns
1996 Tournament Of Towns
(520) 3
(520) 3
Part of
1996 Tournament Of Towns
Problems
(1)
area chasing in convex hexagon
Source: TOT 520 1996 Autumn S A3 Tournament Of Towns
8/16/2024
Let
A
′
,
B
′
,
C
′
,
D
′
,
E
′
A', B', C', D', E'
A
′
,
B
′
,
C
′
,
D
′
,
E
′
and
F
′
F'
F
′
be the midpoints of the sides
A
B
AB
A
B
,
B
C
BC
BC
,
C
D
CD
C
D
,
D
E
DE
D
E
,
E
F
EF
EF
and
F
A
FA
F
A
of an arbitrary convex hexagon
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
respectively. Express the area of
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
in terms of the areas of the triangles
A
B
C
ABC
A
BC
,
B
C
D
′
BCD'
BC
D
′
,
C
D
S
′
CDS'
C
D
S
′
,
D
E
F
′
DEF'
D
E
F
′
,
E
F
A
′
EFA'
EF
A
′
and
F
A
B
′
FAB'
F
A
B
′
.(A Lopshi tz, NB Vassiliev)
geometry
areas
hexagon