Question 151
Let $ABCD$ be a cyclic quadrilateral (a quadrilateral which can be inscribed in a circle). Let $E$ and $F$ be variable points on the sides $AB$ and $CD$, respectively, such that $AE / EB = CF / FD$. Let $P$ be the point on the segment $EF$ such that $PE / PF = AB / CD$. Prove that the ratio between the areas of triangle $APD$ and $BPC$ does not depend on the choice of $E$ and $F$.