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2020 CMIMC
2020 CMIMC Team
15
15
Part of
2020 CMIMC Team
Problems
(1)
2020 Team 15
Source:
2/2/2020
Let
A
B
C
ABC
A
BC
be an acute triangle with
A
B
=
3
AB = 3
A
B
=
3
and
A
C
=
4
AC = 4
A
C
=
4
. Suppose
M
M
M
is the midpoint of segment
B
C
‾
\overline{BC}
BC
,
N
N
N
is the midpoint of
A
M
‾
\overline{AM}
A
M
, and
E
E
E
and
F
F
F
are the feet of the altitudes of
M
M
M
onto
A
B
‾
\overline{AB}
A
B
and
A
C
‾
\overline{AC}
A
C
, respectively. Further suppose
B
C
BC
BC
intersects
N
E
NE
NE
at
S
S
S
and
N
F
NF
NF
at
T
T
T
, and let
X
X
X
and
Y
Y
Y
be the circumcenters of
△
M
E
S
\triangle MES
△
MES
and
△
M
F
T
\triangle MFT
△
MFT
, respectively. If
X
Y
XY
X
Y
is tangent to the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
, what is the area of
△
A
B
C
\triangle ABC
△
A
BC
?
team
2020