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2020 BAMO
4
4
Part of
2020 BAMO
Problems
(1)
2020 BAMO-12: 4
Source:
2/28/2020
Consider
△
A
B
C
\triangle ABC
△
A
BC
. Choose a point
M
M
M
on side
B
C
BC
BC
and let
O
O
O
be the center of the circle passing through the vertices of
△
A
B
M
\triangle ABM
△
A
BM
. Let
k
k
k
be the circle that passes through
A
A
A
and
M
M
M
and whose center lies on
B
C
BC
BC
. Let line
M
O
MO
MO
intersect
K
K
K
again in point
K
K
K
. Prove that the line
B
K
BK
B
K
is the same for any point
M
M
M
on segment
B
C
BC
BC
, so long as all of these constructions are well-defined.Proposed by Evan Chen