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Junior Balkan MO
2015 Junior Balkan MO
3
3
Part of
2015 Junior Balkan MO
Problems
(1)
Jbmo problem 3
Source:
6/26/2015
Let
A
B
C
ABC
A
BC
be an acute triangle.The lines
l
1
l_1
l
1
and
l
2
l_2
l
2
are perpendicular to
A
B
AB
A
B
at the points
A
A
A
and
B
B
B
, respectively.The perpendicular lines from the midpoint
M
M
M
of
A
B
AB
A
B
to the lines
A
C
AC
A
C
and
B
C
BC
BC
intersect
l
1
l_1
l
1
and
l
2
l_2
l
2
at the points
E
E
E
and
F
F
F
, respectively.If
D
D
D
is the intersection point of the lines
E
F
EF
EF
and
M
C
MC
MC
, prove that
∠
A
D
B
=
∠
E
M
F
.
\angle ADB = \angle EMF.
∠
A
D
B
=
∠
EMF
.
geometry