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.
%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.