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National and Regional Contests
Iran Contests
Iran MO (2nd Round)
2018 Iran MO (2nd Round)
1
1
Part of
2018 Iran MO (2nd Round)
Problems
(1)
easy geometry
Source: Iran MO 2018, second round, p1
4/26/2018
Let
P
P
P
be the intersection of
A
C
AC
A
C
and
B
D
BD
B
D
in isosceles trapezoid
A
B
C
D
ABCD
A
BC
D
(
A
B
∥
C
D
AB\parallel CD
A
B
∥
C
D
,
B
C
=
A
D
BC=AD
BC
=
A
D
) . The circumcircle of triangle
A
B
P
ABP
A
BP
inersects
B
C
BC
BC
for the second time at
X
X
X
. Point
Y
Y
Y
lies on
A
X
AX
A
X
such that
D
Y
∥
B
C
DY\parallel BC
D
Y
∥
BC
. Prove that
Y
D
A
^
=
2.
Y
C
A
^
\hat {YDA} =2.\hat {YCA}
Y
D
A
^
=
2.
Y
C
A
^
.
Iran
geometry