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Balkan MO Shortlist
2014 Balkan MO Shortlist
G6
G6
Part of
2014 Balkan MO Shortlist
Problems
(1)
bisector
Source: Balkan MO 2014 G-6
6/10/2015
In
△
A
B
C
\triangle ABC
△
A
BC
with
A
B
=
A
C
AB=AC
A
B
=
A
C
,
M
M
M
is the midpoint of
B
C
BC
BC
,
H
H
H
is the projection of
M
M
M
onto
A
B
AB
A
B
and
D
D
D
is arbitrary point on the side
A
C
AC
A
C
.Let
E
E
E
be the intersection point of the parallel line through
B
B
B
to
H
D
HD
HD
with the parallel line through
C
C
C
to
A
B
AB
A
B
.Prove that
D
M
DM
D
M
is the bisector of
∠
A
D
E
\angle ADE
∠
A
D
E
.
geometry