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National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2019 Junior Balkan Team Selection Tests - Moldova
7
7
Part of
2019 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
Moldova JTST 2019 P7
Source:
4/19/2019
Point
H
H
H
is the orthocenter of the acute triangle
Δ
A
B
C
\Delta ABC
Δ
A
BC
and point
K
K
K
,situated on the line
(
B
C
)
(BC)
(
BC
)
, is the foot of the perpendicular from point
A
A
A
.The circle
Ω
\Omega
Ω
passes through points
A
A
A
and
K
K
K
,intersecting the sides
(
A
B
)
(AB)
(
A
B
)
and
(
A
C
)
(AC)
(
A
C
)
in points
M
M
M
and
N
N
N
.The line that passes through point
A
A
A
and is parallel with
B
C
BC
BC
intersects again the circumcircles of triangles
Δ
A
H
M
\Delta AHM
Δ
A
H
M
and
Δ
A
H
N
\Delta AHN
Δ
A
H
N
in points
X
X
X
and
Y
Y
Y
.Prove that
X
Y
=
B
C
XY =BC
X
Y
=
BC
.
geometry