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Baltic Way
1999 Baltic Way
15
15
Part of
1999 Baltic Way
Problems
(1)
AB = DE ,Nice
Source: Baltic Way 1999
9/1/2008
Let
A
B
C
ABC
A
BC
be a triangle with
∠
C
=
6
0
∘
\angle C=60^\circ
∠
C
=
6
0
∘
and
A
C
<
B
C
AC<BC
A
C
<
BC
. The point
D
D
D
lies on the side
B
C
BC
BC
and satisfies
B
D
=
A
C
BD=AC
B
D
=
A
C
. The side
A
C
AC
A
C
is extended to the point
E
E
E
where
A
C
=
C
E
AC=CE
A
C
=
CE
. Prove that
A
B
=
D
E
AB=DE
A
B
=
D
E
.
trigonometry
geometry
geometric transformation
rotation
geometry proposed