CWMO 2005 Problem 2

Given three points $P$ , $A$ , $B$ and a circle such that the lines $PA$ and $PB$ are tangent to the circle at the points $A$ and $B$ , respectively. A line through the point $P$ intersects that circle at two points $C$ and $D$ . Through the point $B$ , draw a line parallel to $PA$ ; let this line intersect the lines $AC$ and $AD$ at the points $E$ and $F$ , respectively. Prove that $BE = BF$ .