IMO Shortlist 1978 problem 13

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Dodao/la: arhiva
2. travnja 2012.
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.
Izvor: Međunarodna matematička olimpijada, shortlist 1978