Question 19
Given a point $P$ in space and 1979 lines $L_1$, $L_2$, ..., $L_{1979}$ containing it. No two lines are perpendicular. $P_1$ is a point on $L_1$. Show that we can find a point $A_n$ on $L_n$ (for $n = 2$, $3$, ..., $1979$) such that the following 1979 pairs of lines are all perpendicular: $A_{n-1}A_{n+1}$ and $L_n$ for $n = 1$, ..., $1979$. [We regard $A_{-1}$ as $A_{1979}$ and $A_{1980}$ as $A_1$.]