Question 35
$L$ and $L'$ are two perpendicular lines not in the same plane. $AA'$ is perpendicular to both lines, where $A$ belongs to $L$ and $A'$ belongs to $L'$. $S$ is the sphere with diameter $AA'$. For which points $P$ on $S$ can we find points $X$ on $L$ and $X'$ on $L'$ such that $XX'$ touches $S$ at $P$?