MathNet 2025-part-02 — 186 problems (EN–VI) Question 29

Let $ABCD$ be a rectangle and $M$ the midpoint of the side $AD$. Construct the equilateral triangle $DME$, with $E$ and $B$ on the same side of the line $MD$, and the equilateral triangle $BEF$, with $M$ and $F$ on opposite sides of the line $BE$. Show that if the midpoint of the segment $MF$ lies on the line $AC$, then $ABCD$ is a square.
Adrian Bud