Difference between revisions of "1978 IMO Problems/Problem 2"
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| − | + | ==Problem== | |
| + | We consider a fixed point <math>P</math> in the interior of a fixed sphere<math>.</math> We construct three segments <math>PA, PB,PC</math>, perpendicular two by two<math>,</math> with the vertexes <math>A, B, C</math> on the sphere<math>.</math> We consider the vertex <math>Q</math> which is opposite to <math>P</math> in the parallelepiped (with right angles) with <math>PA, PB, PC</math> as edges<math>.</math> Find the locus of the point <math>Q</math> when <math>A, B, C</math> take all the positions compatible with our problem. | ||
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| + | ==Solution== | ||
| + | {{solution}} | ||
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| + | == See Also == {{IMO box|year=1978|num-b=1|num-a=3}} | ||
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| + | [[Category:3D Geometry Problems]] | ||
| + | [[Category:Olympiad Geometry Problems]] | ||
Revision as of 17:00, 29 January 2021
Problem
We consider a fixed point 
in the interior of a fixed sphere
We construct three segments 
, perpendicular two by two
with the vertexes 
on the sphere We consider the vertex 
which is opposite to in the parallelepiped (with right angles) with 
as edges Find the locus of the point when take all the positions compatible with our problem.
Solution
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See Also
| 1978 IMO (Problems) • Resources | ||
| Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
| All IMO Problems and Solutions | ||
