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Old Kyiv MO Geometry
Kyiv City MO Seniors 2003+ geometry
2019.11.2
2019.11.2
Part of
Kyiv City MO Seniors 2003+ geometry
Problems
(1)
\sqrt2 KM > AB, midpoint of broken BAC (2019 Kyiv City MO 11.2)
Source:
9/16/2020
In an acute-angled triangle
A
B
C
ABC
A
BC
, in which
A
B
<
A
C
AB<AC
A
B
<
A
C
, the point
M
M
M
is the midpoint of the side
B
C
,
K
BC, K
BC
,
K
is the midpoint of the broken line segment
B
A
C
BAC
B
A
C
. Prove that
2
K
M
>
A
B
\sqrt2 KM > AB
2
K
M
>
A
B
. (George Naumenko)
geometry
midpoint
geometric inequality