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Japan MO Finals
2016 Japan MO Finals
2
2
Part of
2016 Japan MO Finals
Problems
(1)
2016 Japan Mathematical Olympiad Finals, Problem 2
Source:
2/17/2016
Let
A
B
C
D
ABCD
A
BC
D
be a concyclic quadrilateral such that
A
B
:
A
D
=
C
D
:
C
B
.
AB:AD=CD:CB.
A
B
:
A
D
=
C
D
:
CB
.
The line
A
D
AD
A
D
intersects the line
B
C
BC
BC
at
X
X
X
, and the line
A
B
AB
A
B
intersects the line
C
D
CD
C
D
at
Y
Y
Y
. Let
E
,
F
,
G
E,\ F,\ G
E
,
F
,
G
and
H
H
H
are the midpoints of the edges
A
B
,
B
C
,
C
D
AB,\ BC,\ CD
A
B
,
BC
,
C
D
and
D
A
DA
D
A
respectively. The bisector of angle
A
X
B
AXB
A
XB
intersects the segment
E
G
EG
EG
at
S
S
S
, and that of angle
A
Y
D
AYD
A
Y
D
intersects the segment
F
H
FH
F
H
at
T
T
T
. Prove that the lines
S
T
ST
ST
and
B
D
BD
B
D
are pararell.
geometry