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National and Regional Contests
Iran Contests
Iran MO (2nd Round)
2019 Iran MO (2nd Round)
2
2
Part of
2019 Iran MO (2nd Round)
Problems
(1)
Geometry, Iran MO 2019
Source: Iran MO 2019, secound round, day 1, p2
5/2/2019
A
B
C
ABC
A
BC
is an isosceles triangle (
A
B
=
A
C
AB=AC
A
B
=
A
C
). Point
X
X
X
is an arbitrary point on
B
C
BC
BC
.
Z
∈
A
C
Z \in AC
Z
∈
A
C
and
Y
∈
A
B
Y \in AB
Y
∈
A
B
such that
∠
B
X
Y
=
∠
Z
X
C
\angle BXY = \angle ZXC
∠
BX
Y
=
∠
ZXC
. A line parallel to
Y
Z
YZ
Y
Z
passes through
B
B
B
and cuts
X
Z
XZ
XZ
at
T
T
T
. Prove that
A
T
AT
A
T
bisects
∠
A
\angle A
∠
A
.
geometry