Difference between revisions of "1964 IMO Problems/Problem 6"
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+ | Let <math>A_{2}</math> be the point where line <math>AD_{0}</math> intersects line <math>BC</math> | ||
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+ | Let <math>B_{2}</math> be the point where line <math>BD_{0}</math> intersects line <math>AC</math> | ||
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+ | Let <math>C_{2}</math> be the point where line <math>CD_{0}</math> intersects line <math>AB</math> | ||
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{{solution}} | {{solution}} | ||
Revision as of 23:40, 16 November 2023
Problem
In tetrahedron , vertex
is connected with
, the centroid 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
Let be the point where line
intersects line
Let be the point where line
intersects line
Let be the point where line
intersects line
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See Also
1964 IMO (Problems) • Resources | ||
Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last Question |
All IMO Problems and Solutions |