Question 133
In $\triangle PBC$, $\angle PBC = 60^\circ$. The tangent at point $P$ to the circumcircle $w$ of $\triangle PBC$ intersects with line $CB$ at $A$. Points $D$ and $E$ lie on the line segment $PA$ and circle $w$ respectively, such that $\angle DBE = 90^\circ$ and $PD = PE$. $BE$ and $PC$ meet at $F$. It is given that lines $AF$, $BP$ and $CD$ are concurrent.
(1) Prove that $BF$ is the bisector of $\angle PBC$;
(2) Find the value of $\tan \angle PCB$.
(1) Prove that $BF$ is the bisector of $\angle PBC$;
(2) Find the value of $\tan \angle PCB$.