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National and Regional Contests
Romania Contests
JBMO TST - Romania
2012 Junior Balkan Team Selection Tests - Romania
2012 Junior Balkan Team Selection Tests - Romania
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JBMO TST - Romania
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A'N // B'C', touchpoints of incircle related
Let
A
B
C
ABC
A
BC
be a triangle and
A
′
,
B
′
,
C
′
A', B', C'
A
′
,
B
′
,
C
′
the points in which its incircle touches the sides
B
C
,
C
A
,
A
B
BC, CA, AB
BC
,
C
A
,
A
B
, respectively. We denote by
I
I
I
the incenter and by
P
P
P
its projection onto
A
A
′
AA'
A
A
′
. Let
M
M
M
be the midpoint of the line segment
[
A
′
B
′
]
[A'B']
[
A
′
B
′
]
and
N
N
N
be the intersection point of the lines
M
P
MP
MP
and
A
C
AC
A
C
. Prove that
A
′
N
A'N
A
′
N
is parallel to
B
′
C
′
B'C'
B
′
C
′
3
4
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