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International Contests
Baltic Way
2019 Baltic Way
13
13
Part of
2019 Baltic Way
Problems
(1)
Perpendicular diagonals in a hexagon
Source: 2019 Baltic Way P13
11/18/2019
Let
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
be a convex hexagon in which
A
B
=
A
F
AB=AF
A
B
=
A
F
,
B
C
=
C
D
BC=CD
BC
=
C
D
,
D
E
=
E
F
DE=EF
D
E
=
EF
and
∠
A
B
C
=
∠
E
F
A
=
9
0
∘
\angle ABC = \angle EFA = 90^{\circ}
∠
A
BC
=
∠
EF
A
=
9
0
∘
. Prove that
A
D
⊥
C
E
AD\perp CE
A
D
⊥
CE
.
geometry