We consider a fixed point
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
in the interior of a fixed sphere
![.](/media/m/b/d/d/bdd5ec3ff70fef87f72128d28ab734d1.png)
We construct three segments
![PA, PB,PC](/media/m/c/7/6/c76956555ab60113a4aa35702d3c789f.png)
, perpendicular two by two
![,](/media/m/c/c/6/cc6a28b756c2449c071b10d734c2e4c7.png)
with the vertexes
![A, B, C](/media/m/5/2/5/5251ced8c37ecf5247e7f644e571612f.png)
on the sphere
![.](/media/m/b/d/d/bdd5ec3ff70fef87f72128d28ab734d1.png)
We consider the vertex
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
which is opposite to
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
in the parallelepiped (with right angles) with
![PA, PB, PC](/media/m/1/3/7/137e4a15c464ba9ac32df0940dda85a5.png)
as edges
![.](/media/m/b/d/d/bdd5ec3ff70fef87f72128d28ab734d1.png)
Find the locus of the point
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
when
![A, B, C](/media/m/5/2/5/5251ced8c37ecf5247e7f644e571612f.png)
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.