MathNet 2019-part-07 — 184 problems (EN–VI) Question 124

Let $ABC$ be an acute angle triangle, where $AB \lt AC$, and let $M$ be the midpoint of $BC$, and $K$ be the midpoint of the polygonal chain $BAC$. Show that $\sqrt{2} KM \gt AB$.

(Heorhii Naumenko)