Question 10
In isosceles triangle $ABC$ with $AB=AC$, extend $CB$ through $B$ to $P$. A line through $P$, parallel to altitude $BF$, meets $AC$ at $D$, where $D$ lies between $A$ and $F$. From $P$, draw a perpendicular to the extension of $AB$ at $E$, with $B$ between $E$ and $A$. Express $BF$ in terms of $PD$ and $PE$.
