Question 7
Let $ABCD$ be a cyclic quadrilateral. Let $M,N$ be the midpoints of $AC,BD$, respectively, and let $E=AB\cap CD$, $F=AD\cap BC$. Prove that
$$\frac{2MN}{EF}=\left|\frac{AC}{BD}-\frac{BD}{AC}\right|.$$
$$\frac{2MN}{EF}=\left|\frac{AC}{BD}-\frac{BD}{AC}\right|.$$