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Baltic Way
2022 Baltic Way
11
11
Part of
2022 Baltic Way
Problems
(1)
Two circles through A and O
Source: Baltic Way 2022/11
11/12/2022
Let
A
B
C
ABC
A
BC
be a triangle with circumcircle
Γ
\Gamma
Γ
and circumcentre
O
O
O
. The circle with centre on the line
A
B
AB
A
B
and passing through the points
A
A
A
and
O
O
O
intersects
Γ
\Gamma
Γ
again in
D
D
D
. Similarly, the circle with centre on the line
A
C
AC
A
C
and passing through the points
A
A
A
and
O
O
O
intersects
Γ
\Gamma
Γ
again in
E
E
E
. Prove that
B
D
BD
B
D
is parallel with
C
E
CE
CE
.
geometry