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Common chords are concurrent

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September 13, 2010
conicsellipsegeometry proposedgeometryconcurrency

Problem Statement

Let E1,E2E_1, E_2, and E3E_3 be three mutually intersecting ellipses, all in the same plane. Their foci are respectively F2,F3;F3,F1F_2, F_3; F_3, F_1; and F1,F2F_1, F_2. The three foci are not on a straight line. Prove that the common chords of each pair of ellipses are concurrent.
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