BG-MO 1984 Problem 6

Let there be given a pyramid $SABCD$ whose base $ABCD$ is a parallelogram. Let $N$ be the midpoint of $BC$ . A plane $\lambda$ intersects the lines $SC,SA,AB$ at points $P,Q,R$ respectively such that $\overline{CP}/\overline{CS}=\overline{SQ}/\overline{SA}=\overline{AR}/\overline{AB}$ . A point $M$ on the line $SD$ is such that the line $MN$ is parallel to $\lambda$ . Show that the locus of points $M$ , when $\lambda$ takes all possible positions, is a segment of the length $\frac{\sqrt5}2SD$ .