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Balkan MO
2020 Balkan MO
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2020 Balkan MO
Problems
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Problem 1, BMO 2020
Source: Problem 1, BMO 2020
11/1/2020
Let
A
B
C
ABC
A
BC
be an acute triangle with
A
B
=
A
C
AB=AC
A
B
=
A
C
, let
D
D
D
be the midpoint of the side
A
C
AC
A
C
, and let
γ
\gamma
γ
be the circumcircle of the triangle
A
B
D
ABD
A
B
D
. The tangent of
γ
\gamma
γ
at
A
A
A
crosses the line
B
C
BC
BC
at
E
E
E
. Let
O
O
O
be the circumcenter of the triangle
A
B
E
ABE
A
BE
. Prove that midpoint of the segment
A
O
AO
A
O
lies on
γ
\gamma
γ
.Proposed by Sam Bealing, United Kingdom
geometry
BMO