Let A B C D be a cyclic quadrilateral (a quadrilateral which can be inscribed in a circle). Let E and F be variable points on the sides A B and C D, respectively, such that A E / E B=C F / F D. Let P be the point on the segment E F such that P E / P F=A B / C D. Prove that the ratio between the areas of triangle A P D and B P C does not depend on the choice of E and F.
