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Turkey Junior National Olympiad
2021 Turkey Junior National Olympiad
4
4
Part of
2021 Turkey Junior National Olympiad
Problems
(1)
parallel lines given, proving tangency
Source: Turkey Junior National Olympiad 2021 P4
1/7/2022
Let
X
X
X
be a point on the segment
[
B
C
]
[BC]
[
BC
]
of an equilateral triangle
A
B
C
ABC
A
BC
and let
Y
Y
Y
and
Z
Z
Z
be points on the rays
[
B
A
[BA
[
B
A
and
[
C
A
[CA
[
C
A
such that the lines
A
X
,
B
Z
,
C
Y
AX, BZ, CY
A
X
,
BZ
,
C
Y
are parallel. If the intersection of
X
Y
XY
X
Y
and
A
C
AC
A
C
is
M
M
M
and the intersection of
X
Z
XZ
XZ
and
A
B
AB
A
B
is
N
N
N
, prove that
M
N
MN
MN
is tangent to the incenter of
A
B
C
ABC
A
BC
.
geometry
tangent