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Saint Petersburg Mathematical Olympiad
2013 Saint Petersburg Mathematical Olympiad
3
St.Peterburg, P3 Grade 11, 2013
St.Peterburg, P3 Grade 11, 2013
Source:
April 17, 2014
geometry
3D geometry
tetrahedron
parallelogram
geometry proposed
Problem Statement
Let
M
M
M
and
N
N
N
are midpoint of edges
A
B
AB
A
B
and
C
D
CD
C
D
of the tetrahedron
A
B
C
D
ABCD
A
BC
D
,
A
N
=
D
M
AN=DM
A
N
=
D
M
and
C
M
=
B
N
CM=BN
CM
=
BN
. Prove that
A
C
=
B
D
AC=BD
A
C
=
B
D
. S. Berlov
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