Question 1
Let $ABCD$ be a quadrilateral whose sides are all equal and $\angle ABC=60^\circ$. Let $\ell$ pass through $D$ without meeting the quadrilateral elsewhere. Let $E,F$ be the intersections of $\ell$ with the lines $AB,BC$, respectively, and let $M=CE\cap AF$. Prove that $CA^2=CM\cdot CE$.
