IMO 1985 LL GBR31

Let E1, E2, and E3 be three mutually intersecting ellipses, all

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IMO 1985 LL GBR31

Origin: GBR

Problem

Let E1, E2, and E3 be three mutually intersecting ellipses, all in the same plane. Their foci are respectively F2, F3; F3, F1; and F1, F2. The three foci are not on a straight line. Prove that the common chords of each pair of ellipses are concurrent.