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2019 Stanford Mathematics Tournament
7
7
Part of
2019 Stanford Mathematics Tournament
Problems
(1)
SMT 2019 Geometry #7
Source:
8/8/2023
Let
G
G
G
be the centroid of triangle
A
B
C
ABC
A
BC
with
A
B
=
9
AB = 9
A
B
=
9
,
B
C
=
10
,
BC = 10,
BC
=
10
,
and
A
C
=
17
AC = 17
A
C
=
17
. Denote
D
D
D
as the midpoint of
B
C
BC
BC
. A line through
G
G
G
parallel to
B
C
BC
BC
intersects
A
B
AB
A
B
at
M
M
M
and
A
C
AC
A
C
at
N
N
N
. If
B
G
BG
BG
intersects
C
M
CM
CM
at
E
E
E
and
C
G
CG
CG
intersects
B
N
BN
BN
at
F
F
F
, compute the area of triangle
D
E
F
DEF
D
EF
.
geometry