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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2020 Moldova Team Selection Test
9
9
Part of
2020 Moldova Team Selection Test
Problems
(1)
Show that angle BMN=90
Source: Moldova TST 2020
3/7/2020
Let
Δ
A
B
C
\Delta ABC
Δ
A
BC
be an acute triangle and
Ω
\Omega
Ω
its circumscribed circle, with diameter
A
P
AP
A
P
. Points
E
E
E
and
F
F
F
are the orthogonal projections from
B
B
B
on
A
C
AC
A
C
and
A
P
AP
A
P
, points
M
M
M
and
N
N
N
are the midpoints of segments
E
F
EF
EF
and
C
P
CP
CP
. Prove that
∠
B
M
N
=
90
\angle BMN=90
∠
BMN
=
90
.
geometry