Question 14
Let $NS$ and $EW$ be two perpendicular diameters of a circle $\mathcal{C}$. A line $l$ touches $\mathcal{C}$ at point $S$. Let $A$ and $B$ be two points on $\mathcal{C}$, symmetric with respect to the diameter $EW$. Denote the intersection points of $l$ with the lines $NA$ and $NB$ by $A'$ and $B'$, respectively. Show that $|SA'| \cdot |SB'| = |SN|^2$.