ILL 1985 Problem 31

Let $E_1, E_2$ , and $E_3$ be three mutually intersecting ellipses, all in the same plane. Their foci are respectively $F_2, F_3; F_3, F_1$ ; and $F_1, F_2$ . The three foci are not on a straight line. Prove that the common chords of each pair of ellipses are concurrent.