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Balkan MO Shortlist
2023 Balkan MO Shortlist
G5
G5
Part of
2023 Balkan MO Shortlist
Problems
(1)
Another config geo with concurrent lines
Source: BMO SL 2023 G5
5/3/2024
Let
A
B
C
ABC
A
BC
be a triangle with circumcenter
O
O
O
. Point
X
X
X
is the intersection of the parallel line from
O
O
O
to
A
B
AB
A
B
with the perpendicular line to
A
C
AC
A
C
from
C
C
C
. Let
Y
Y
Y
be the point where the external bisector of
∠
B
X
C
\angle BXC
∠
BXC
intersects with
A
C
AC
A
C
. Let
K
K
K
be the projection of
X
X
X
onto
B
Y
BY
B
Y
. Prove that the lines
A
K
,
X
O
,
B
C
AK, XO, BC
A
K
,
XO
,
BC
have a common point.
geometry
AZE BMO TST
TST