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Problems
Contests
International Contests
IMO Longlists
1972 IMO Longlists
13
13
Part of
1972 IMO Longlists
Problems
(1)
Set of points A with a given sphere
Source:
11/3/2010
Given a sphere
K
K
K
, determine the set of all points
A
A
A
that are vertices of some parallelograms
A
B
C
D
ABCD
A
BC
D
that satisfy
A
C
≤
B
D
AC \le BD
A
C
≤
B
D
and whose entire diagonal
B
D
BD
B
D
is contained in
K
K
K
.
geometry
3D geometry
sphere
parallelogram
geometry unsolved