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2014 Balkan MO Shortlist
G1
G1
Part of
2014 Balkan MO Shortlist
Problems
(1)
Balkan MO 2014 shortlist-G1
Source: Balkan MO 2014 shortlist-G1
6/10/2015
Let
A
B
C
ABC
A
BC
be an isosceles triangle, in which
A
B
=
A
C
AB=AC
A
B
=
A
C
, and let
M
M
M
and
N
N
N
be two points on the sides
B
C
BC
BC
and
A
C
AC
A
C
, respectively such that
∠
B
A
M
=
∠
M
N
C
\angle BAM = \angle MNC
∠
B
A
M
=
∠
MNC
. Suppose that the lines
M
N
MN
MN
and
A
B
AB
A
B
intersects at
P
P
P
. Prove that the bisectors of the angles
∠
B
A
M
\angle BAM
∠
B
A
M
and
∠
B
P
M
\angle BPM
∠
BPM
intersects at a point lying on the line
B
C
BC
BC
geometry