such that 
and 
with another positive integer 
,
is a perfect square. For example, if the number on the blackboard is 
,
,
,
,
.
,
with circumcenter 
and orthocenter 
,
be an arbitrary point on the circumcircle of triangle 
and that line 
is not parallel to line 
.
be the point on the circumcircle of triangle 
is perpendicular to 
be the point on line 
such that 
.
be the points on the circumcircle of triangle 
is a diameter, and 
and 
are parallel. Let 
be the midpoint of 
.
and 
are perpendicular.
and 
are perpendicular.
Y by Adventure10, Mango247
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.
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.
?
