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Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2017 Dutch BxMO TST
3
3
Part of
2017 Dutch BxMO TST
Problems
(1)
parallelism
Source: Netherlands TST for Bxmo 2017, problem 3
2/1/2018
Let
A
B
C
ABC
A
BC
be a triangle with
∠
A
=
90
\angle A = 90
∠
A
=
90
and let
D
D
D
be the orthogonal projection of
A
A
A
onto
B
C
BC
BC
. The midpoints of
A
D
AD
A
D
and
A
C
AC
A
C
are called
E
E
E
and
F
F
F
, respectively. Let
M
M
M
be the circumcentre of
B
E
F
BEF
BEF
. Prove that
A
C
AC
A
C
and
B
M
BM
BM
are parallel.
geometry