We consider a fixed point
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in the interior of a fixed sphere
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We construct three segments
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, perpendicular two by two
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with the vertexes
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on the sphere
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We consider the vertex
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which is opposite to
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in the parallelepiped (with right angles) with
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as edges
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Find the locus of the point
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when
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take all the positions compatible with our problem.
%V0
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.