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National and Regional Contests
Poland Contests
Polish MO Finals
1960 Polish MO Finals
3
3
Part of
1960 Polish MO Finals
Problems
(1)
parallel in cyclic hexagon
Source: Polish MO Finals 1960 p3
8/30/2024
On the circle 6 distinct points
A
A
A
,
B
B
B
,
C
C
C
,
D
D
D
,
E
E
E
,
F
F
F
are chosen in such a way that
A
B
AB
A
B
is parallel to
D
E
DE
D
E
, and
D
C
DC
D
C
is parallel to
A
F
AF
A
F
. Prove that
B
C
BC
BC
is parallel to
E
F
EF
EF
geometry
hexagon
Cyclic