Question 106
Let $ABC$ be an isosceles triangle with $AB = AC$. Let $D$ and $E$ be the feet of the perpendiculars from $B$ and $C$ to $\overline{AC}$ and $\overline{AB}$, respectively. Suppose that $\overline{CE}$ and $\overline{BD}$ intersect at point $H$. If $EH = 1$ and $AD = 4$, find $DE$.