ILL 1987 Problem 62

Let $l, l'$ be two lines in $3$ -space and let $A,B,C$ be three points taken on $l$ with $B$ as midpoint of the segment $AC$ . If $a, b, c$ are the distances of $A,B,C$ from $l'$ , respectively, show that $b \leq \sqrt{ \frac{a^2+c^2}{2}}$ , equality holding if $l, l'$ are parallel.

Attachments: