Difference between revisions of "1964 IMO Problems/Problem 6"
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== Solution == | == Solution == | ||
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+ | == See Also == | ||
+ | {{IMO box|year=1964|num-b=5|After=Last Question}} | ||
[[Category:Olympiad Geometry Problems]] | [[Category:Olympiad Geometry Problems]] | ||
[[Category:3D Geometry Problems]] | [[Category:3D Geometry Problems]] |
Revision as of 11:49, 29 January 2021
Problem
In tetrahedron , vertex
is connected with
, the centrod of
. Lines parallel to
are drawn through
and
. These lines intersect the planes
and
in points
and
, respectively. Prove that the volume of
is one third the volume of
. Is the result true if point
is selected anywhere within
?
Solution
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See Also
1964 IMO (Problems) • Resources | ||
Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by [[1964 IMO Problems/Problem {{{num-a}}}|Problem {{{num-a}}}]] |
All IMO Problems and Solutions |