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2013 IMO Shortlist
G5
G5
Part of
2013 IMO Shortlist
Problems
(1)
IMO Shortlist 2013, Geometry #5
Source: IMO Shortlist 2013, Geometry #5
7/10/2014
Let
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
be a convex hexagon with
A
B
=
D
E
AB=DE
A
B
=
D
E
,
B
C
=
E
F
BC=EF
BC
=
EF
,
C
D
=
F
A
CD=FA
C
D
=
F
A
, and
∠
A
−
∠
D
=
∠
C
−
∠
F
=
∠
E
−
∠
B
\angle A-\angle D = \angle C -\angle F = \angle E -\angle B
∠
A
−
∠
D
=
∠
C
−
∠
F
=
∠
E
−
∠
B
. Prove that the diagonals
A
D
AD
A
D
,
B
E
BE
BE
, and
C
F
CF
CF
are concurrent.
geometry
complex numbers
hexagon
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