Question 40
Consider a tetrahedron $ABCD$ and the points $M, N$ on the edges $AC$ and $BD$, respectively. Prove that for any point $P$ of the segment $MN$, $P \neq M$, $P \neq N$, there exists a unique pair of points $(X, Y)$, with $X$ and $Y$ on the edges $AB$ and $CD$, respectively, such that the points $X, P$ and $Y$ are collinear.