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Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2010.8.5
2010.8.5
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
(MB- MS)(NC-NS) <= 0, midpoints (Kyiv City Olympiad 2010 8.5)
Source:
7/2/2020
In an acute-angled triangle
A
B
C
ABC
A
BC
, the points
M
M
M
and
N
N
N
are the midpoints of the sides
A
B
AB
A
B
and
A
C
AC
A
C
, respectively. For an arbitrary point
S
S
S
lying on the side of
B
C
BC
BC
prove that the condition holds
(
M
B
−
M
S
)
(
N
C
−
N
S
)
≤
0
(MB- MS)(NC-NS) \le 0
(
MB
−
MS
)
(
NC
−
NS
)
≤
0
geometry
midpoints
geometric inequality