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Moscow Mathematical Olympiad
1955 Moscow Mathematical Olympiad
301
301
Part of
1955 Moscow Mathematical Olympiad
Problems
(1)
MMO 301 Moscow MO 1955 <OAB, <OBA, <OBC, <OCB,<OAC,<OCA acute, trihedral
Source:
8/17/2019
Given a trihedral angle with vertex
O
O
O
. Find whether there is a planar section
A
B
C
ABC
A
BC
such that the angles
∠
O
A
B
\angle OAB
∠
O
A
B
,
∠
O
B
A
\angle OBA
∠
OB
A
,
∠
O
B
C
\angle OBC
∠
OBC
,
∠
O
C
B
\angle OCB
∠
OCB
,
∠
O
A
C
\angle OAC
∠
O
A
C
,
∠
O
C
A
\angle OCA
∠
OC
A
are acute.
trihedral angle
angles
acute
3D geometry
geometry