MathNet 2017-part-05 — 176 problems (EN–VI) Question 41

Let $ABCD$ be a square. We take the points $E \in (AB)$, $N \in (CD)$ and $F, M \in (BC)$, such that the triangles $AMN$ and $DEF$ are equilateral. Prove that $PQ = FM$, where $\{P\} = AN \cap DE$ and $\{Q\} = AM \cap EF$.