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Poland - First Round
1992 Poland - First Round
3
3
Part of
1992 Poland - First Round
Problems
(1)
Hexagon with a center of symmetry
Source: Poland Math Olympiad 1992 First Round #3
6/2/2023
Given is a hexagon
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
with a center of symmetry. The lines
A
B
AB
A
B
and
E
F
EF
EF
meet at the point
A
′
A'
A
′
, the lines
B
C
BC
BC
and
A
F
AF
A
F
meet at the point
B
′
B'
B
′
, and the lines
A
B
AB
A
B
and
C
D
CD
C
D
meet at the point
C
′
C'
C
′
. Prove that
A
B
⋅
B
C
⋅
C
D
=
A
A
′
⋅
B
B
′
⋅
C
C
′
AB \cdot BC \cdot CD = AA' \cdot BB' \cdot CC'
A
B
⋅
BC
⋅
C
D
=
A
A
′
⋅
B
B
′
⋅
C
C
′
.
symmetry