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1982 IMO Longlists
50
50
Part of
1982 IMO Longlists
Problems
(1)
the sum of dihedral angles equals 2 pi (ILL 1982 - P50)
Source:
5/16/2011
Let
O
O
O
be the midpoint of the axis of a right circular cylinder. Let
A
A
A
and
B
B
B
be diametrically opposite points of one base, and
C
C
C
a point of the other base circle that does not belong to the plane
O
A
B
OAB
O
A
B
. Prove that the sum of dihedral angles of the trihedral
O
A
B
C
OABC
O
A
BC
is equal to
2
π
2\pi
2
π
.
geometry