Let
be a regular tetrahedron. To an arbitrary point
on one edge, say
, corresponds the point
which is the intersection of two lines
and
, drawn from
orthogonally to
and from
orthogonally to
. What is the locus of
when
varies ?
%V0
Let $ABCD$ be a regular tetrahedron. To an arbitrary point $M$ on one edge, say $CD$, corresponds the point $P = P(M)$ which is the intersection of two lines $AH$ and $BK$, drawn from $A$ orthogonally to $BM$ and from $B$ orthogonally to $AM$. What is the locus of $P$ when $M$ varies ?
Školjka