1967 IMO Problems/Problem 2
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Prove that iff. one edge of a tetrahedron is less than ; then its volume is less than or equal to
.
Solution
Assume and let
. Let
be the feet of perpendicular from
to
and
and from
to
, respectively.
Suppose . We have that
,
. We also have
. So the volume of the tetrahedron is
.
We want to prove that this value is at most , which is equivalent to
. This is true because
.
The above solution was posted and copyrighted by jgnr. The original thread can be found here: [1]
See Also
1967 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |