AUSTRIAN-POLISH 1998 Problem 6

Different points $A,B,C,D,E,F$ lie on circle $k$ in this order. The tangents to $k$ in the points $A$ and $D$ and the lines $BF$ and $CE$ have a common point $P$ . Prove that the lines $AD,BC$ and $EF$ also have a common point or are parallel.