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National and Regional Contests
Poland Contests
Poland - Second Round
2020 Poland - Second Round
3.
3.
Part of
2020 Poland - Second Round
Problems
(1)
Geometry
Source: Poland - Second Round P3
2/8/2020
Let
M
M
M
be the midpoint of the side
B
C
BC
BC
of a acute triangle
A
B
C
ABC
A
BC
. Incircle of the triangle
A
B
M
ABM
A
BM
is tangent to the side
A
B
AB
A
B
at the point
D
D
D
. Incircle of the triangle
A
C
M
ACM
A
CM
is tangent to the side
A
C
AC
A
C
at the point
E
E
E
. Let
F
F
F
be the such point, that the quadrilateral
D
M
E
F
DMEF
D
MEF
is a parallelogram. Prove that
F
F
F
lies on the bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
.
geometry
parallelogram