Difference between revisions of "1978 IMO Problems/Problem 2"

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==Problem==
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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==
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{{solution}}
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== See Also == {{IMO box|year=1978|num-b=1|num-a=3}}

Revision as of 16:59, 29 January 2021

Problem

We consider a fixed point $P$ in the interior of a fixed sphere$.$ We construct three segments $PA, PB,PC$, perpendicular two by two$,$ with the vertexes $A, B, C$ on the sphere$.$ We consider the vertex $Q$ which is opposite to $P$ in the parallelepiped (with right angles) with $PA, PB, PC$ as edges$.$ Find the locus of the point $Q$ when $A, B, C$ 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
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