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National and Regional Contests
Iran Contests
Iran MO (2nd Round)
2019 Iran MO (2nd Round)
4
4
Part of
2019 Iran MO (2nd Round)
Problems
(1)
Wrong geo?
Source: Iranian second round/Day2/Problem4
5/3/2019
Consider a circle with diameter
A
B
AB
A
B
and let
C
,
D
C,D
C
,
D
be points on its circumcircle such that
C
,
D
C,D
C
,
D
are not in the same side of
A
B
AB
A
B
.Consider the parallel line to
A
C
AC
A
C
passing from
D
D
D
and let it intersect
A
B
AB
A
B
at
E
E
E
.Similarly consider the paralell line to
A
D
AD
A
D
passing from
C
C
C
and let it intersect
A
B
AB
A
B
at
F
F
F
.The perpendicular line to
A
B
AB
A
B
at
E
E
E
intersects
B
C
BC
BC
at
X
X
X
and the perpendicular line to
A
B
AB
A
B
at
F
F
F
intersects
D
B
DB
D
B
at
Y
Y
Y
.Prove that the permiter of triangle
A
X
Y
AXY
A
X
Y
is twice
C
D
CD
C
D
.Remark:This problem is proved to be wrong due to a typo in the exam papers you can find the correct version [url=https://artofproblemsolving.com/community/c6h1832731_geometry__iran_mo_2019]here.
geometry
circumcircle