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Balkan MO
2000 Balkan MO
2
2
Part of
2000 Balkan MO
Problems
(1)
Balkan geo 2000
Source: balkan mathematical olympiads 2000
4/7/2006
Let
A
B
C
ABC
A
BC
be an acute-angled triangle and
D
D
D
the midpoint of
B
C
BC
BC
. Let
E
E
E
be a point on segment
A
D
AD
A
D
and
M
M
M
its projection on
B
C
BC
BC
. If
N
N
N
and
P
P
P
are the projections of
M
M
M
on
A
B
AB
A
B
and
A
C
AC
A
C
then the interior angule bisectors of
∠
N
M
P
\angle NMP
∠
NMP
and
∠
N
E
P
\angle NEP
∠
NEP
are parallel.
geometry solved
geometry