SE-SKOLORNAS 2017 Problem 3

Given the segments $AB$ and $CD$ not necessarily on the same plane. Point $X$ is the midpoint of the segment $AB$ , and the point $Y$ is the midpoint of $CD$ . Given that point $X$ is not on line $CD$ , and that point $Y$ is not on line $AB$ , prove that $2 | XY | \le | AD | + | BC |$ . When is equality achieved?