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Baltic Way
2023 Baltic Way
14
14
Part of
2023 Baltic Way
Problems
(1)
Centroid geo
Source: Baltic Way 2023/14
11/11/2023
Let
A
B
C
ABC
A
BC
be a triangle with centroid
G
G
G
. Let
D
,
E
,
F
D, E, F
D
,
E
,
F
be the circumcenters of triangles
B
C
G
,
C
A
G
,
A
B
G
BCG, CAG, ABG
BCG
,
C
A
G
,
A
BG
. Let
X
X
X
be the intersection of the perpendiculars from
E
E
E
to
A
B
AB
A
B
and from
F
F
F
to
A
C
AC
A
C
. Prove that
D
X
DX
D
X
bisects
E
F
EF
EF
.
geometry