Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that $AP=2AB$. If $\angle BPC=\beta$, then $\tan \beta$ is equal to :

Question

$\begin{array}{1 1} (1) \large\frac{1}{4} \\ (2)\large\frac{2}{9} \\ (3) \large\frac{4}{9} \\ (4) \large\frac{6}{7} \end{array}$