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 $AP = 2 AB$. If $\angle{BPC} = \beta$, then $\tan \beta$ is equal to

Question

( A ) $\frac{2}{9}$
( B ) $\frac{4}{9}$
( C ) $\frac{1}{4}$
( D ) $\frac{6}{7}$