Difference between revisions of "1964 IMO Problems/Problem 6"
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<math>|CC_{2}|=3|D_{0}C_{2}|</math> | <math>|CC_{2}|=3|D_{0}C_{2}|</math> | ||
| − | Since <math>\Delta D_{0}A_{2}A_{1}\sim \Delta AA_{2}A_{1}</math>, then | + | Since <math>\Delta D_{0}A_{2}A_{1}\sim \Delta AA_{2}A_{1}</math>, then <math>|AA_{2}|=|DD_{0}| \frac{|AA_{2}|}{|D_{0}A_{2}|}</math> |
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Revision as of 22:47, 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 
From centroid properties we have:
Since 
, then 
This problem needs a solution. If you have a solution for it, please help us out by adding it.
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 | ||
