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National and Regional Contests
Romania Contests
JBMO TST - Romania
2014 Junior Balkan Team Selection Tests - Romania
2014 Junior Balkan Team Selection Tests - Romania
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JBMO TST - Romania
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orthocenter of triangle XYT lies on BC
Let
D
D
D
and
E
E
E
be the midpoints of sides
[
A
B
]
[AB]
[
A
B
]
and
[
A
C
]
[AC]
[
A
C
]
of the triangle
A
B
C
ABC
A
BC
. The circle of diameter
[
A
B
]
[AB]
[
A
B
]
intersects the line
D
E
DE
D
E
on the opposite side of
A
B
AB
A
B
than
C
C
C
, in
X
X
X
. The circle of diameter
[
A
C
]
[AC]
[
A
C
]
intersects
D
E
DE
D
E
on the opposite side of
A
C
AC
A
C
than
B
B
B
in
Y
Y
Y
. Let
T
T
T
be the intersection of
B
X
BX
BX
and
C
Y
CY
C
Y
. Prove that the orthocenter of triangle
X
Y
T
XY T
X
Y
T
lies on
B
C
BC
BC
.
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