MathDB

31

Part of 1985 IMO Longlists

Problems(1)

Common chords are concurrent

Source:

9/13/2010
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.
conicsellipsegeometry proposedgeometryconcurrency