Let $\triangle A B C$ be an isosceles triangle such that $A B$ and $A C$ are of equal length. $A D$ is the altitude from $A$ on $B C$ and $B E$ is the altitude from $\mathrm{B}$ on $\mathrm{AC}$ . If $\mathrm{AD}$ and $\mathrm{BE}$ intersect at $\mathrm{O}$ such that $\angle \mathrm{AOB}=105^{\circ}$ , then $\frac{A D}{B E}$ equals