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Brianchon's theorem
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==Formal statement== Let <math>P_1P_2P_3P_4P_5P_6</math> be a [[hexagon]] formed by six [[tangent line]]s of a [[conic section]]. Then lines <math>\overline{P_1P_4},\; \overline{P_2P_5},\; \overline{P_3P_6}</math> (extended diagonals each connecting opposite vertices) intersect at a single [[Point (geometry)|point]] <math>B</math>, the '''Brianchon point'''.<ref name=WW>Whitworth, William Allen. ''Trilinear Coordinates and Other Methods of Modern Analytical Geometry of Two Dimensions'', Forgotten Books, 2012 (orig. Deighton, Bell, and Co., 1866). http://www.forgottenbooks.com/search?q=Trilinear+coordinates&t=books</ref>{{rp|p. 218}}<ref>{{cite book | author = Coxeter, H. S. M. | author-link = H. S. M. Coxeter | title = Projective Geometry | edition = 2nd | year = 1987 | publisher = Springer-Verlag | isbn = 0-387-96532-7 | pages = Theorem 9.15, p. 83 | no-pp = true}}</ref>
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