KöMaL 2016 B4785

$\mathcal{G}$ is a given sphere in the space. For any line $e$ that has no common point with $\mathcal{G}$ , define the line $f$ as the conjugate of $e$ with respect to $\mathcal{G}$ if $f$ joins the points of tangency on the two planes tangent to $G$ passing through $e$ . Show that two lines of the space passing $\mathcal{G}$ are skew if and only if their conjugates with respect to $\mathcal{G}$ are skew.