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Moscow Mathematical Olympiad
1953 Moscow Mathematical Olympiad
240
240
Part of
1953 Moscow Mathematical Olympiad
Problems
(1)
MMO 240 Moscow MO 1953 skew segments comparison
Source:
8/9/2019
Let
A
B
AB
A
B
and
A
1
B
1
A_1B_1
A
1
B
1
be two skew segments,
O
O
O
and
O
1
O_1
O
1
their respective midpoints. Prove that
O
O
1
OO_1
O
O
1
is shorter than a half sum of
A
A
1
AA_1
A
A
1
and
B
B
1
BB_1
B
B
1
.
skew
midpoints
geometric inequality
geometry
3D geometry