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All-Russian Olympiad
1980 All Soviet Union Mathematical Olympiad
302
302
Part of
1980 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 302 All Soviet Union MO 1980 tetrahedron , cos (AC,BD) <= |CD|/|AB|
Source:
7/19/2019
The edge
[
A
C
]
[AC]
[
A
C
]
of the tetrahedron
A
B
C
D
ABCD
A
BC
D
is orthogonal to
[
B
C
]
[BC]
[
BC
]
, and
[
A
D
]
[AD]
[
A
D
]
is orthogonal to
[
B
D
]
[BD]
[
B
D
]
. Prove that the cosine of the angle between lines
(
A
C
)
(AC)
(
A
C
)
and
(
B
D
)
(BD)
(
B
D
)
is less than
∣
C
D
∣
/
∣
A
B
∣
|CD|/|AB|
∣
C
D
∣/∣
A
B
∣
.
trigonometry
geometry
tetrahedron
3D geometry
orthogonal