Question 41
Let $ABC$ be a triangle with $\angle A = 90^{\circ}$, $AB = 1$, and $AC = 2$. Let $\ell$ be a line through $A$ perpendicular to $BC$, and let the perpendicular bisectors of $AB$ and $AC$ meet $\ell$ at $E$ and $F$, respectively. Find the length of segment $EF$.