Question 4
Let $ABCD$ be a quadrilateral such that all sides have equal length and angle $\angle ABC$ is $60$ degrees. Let $\ell$ be a line passing through $D$ and not intersecting the quadrilateral (except at $D$). Let $E$ and $F$ be the points of intersection of $\ell$ with $AB$ and $BC$ respectively. Let $M$ be the point of intersection of $CE$ and $AF$.
Prove that $CA^{2} = CM \times CE$.
Prove that $CA^{2} = CM \times CE$.