Question 17
The segment $\overline{AB}$ is the longer side of the rectangle $ABCD$. Let $E$ be the intersection of the perpendicular from $B$ to $\overline{AC}$ and the line $AD$, and let $F$ be the intersection of the circle with centre $A$ which passes through $B$ and $\overline{CD}$. Prove that the lines $AF$ and $EF$ are perpendicular.
