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National and Regional Contests
Azerbaijan Contests
Azerbaijan Junior National Olympiad
2020 Azerbaijan National Olympiad
4
4
Part of
2020 Azerbaijan National Olympiad
Problems
(1)
Problem 4
Source: Azerbaijan third round 2020
6/6/2020
There is a non-equilateral triangle
A
B
C
ABC
A
BC
.Let
A
B
C
ABC
A
BC
's Incentri
I
I
I
.Point
D
D
D
is on the
B
C
BC
BC
side.The circle drawn outside the triangle
I
B
D
IBD
I
B
D
and
I
C
D
ICD
I
C
D
intersects the sides
A
B
AB
A
B
and
A
C
AC
A
C
at points
E
E
E
and
F
.
F.
F
.
The circle drawn outside the triangle
D
E
F
DEF
D
EF
intersects the sides
A
B
AB
A
B
and
A
C
AC
A
C
at
N
N
N
and
M
M
M
.Prove that
E
M
∥
F
N
EM\parallel FN
EM
∥
FN
.
geometry