Theorem: Let X, Y, Z be three points on a conic C, and l a line not passing through X, Y or Z. Let L ≡ YZ.l; M ≡ ZX.l; N ≡ XY.l. The tangents from L to C touch C at A and A', those from M touch C at B, B'; from N touch at C, C'. Then these contact points can be labelled so that XA, YB, ZC are concurrent, as are the triples XA, YB', ZC'; XA', YB, ZC'; and XA', YB', ZC.
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BMO conic generalization & proof by Michael Fox
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Created by Michael de Villiers, 30 Oct 2010; updated to WebSketchpad, 7 May 2021.