Question 110
In ellipse $\Gamma$, $A$ is an endpoint of the major axis, $B$ is an endpoint of the minor axis, and $F_1, F_2$ are the foci. If $\overrightarrow{AF_1} \cdot \overrightarrow{AF_2} + \overrightarrow{BF_1} \cdot \overrightarrow{BF_2} = 0$, then the value of $\frac{|AB|}{|F_1F_2|}$ is ______.