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Brianchon's theorem
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==Degenerations== [[File:Brianchon-3-tangents.svg|300px|thumb|3-tangents degeneration of Brianchon's theorem]] As for Pascal's theorem there exist ''degenerations'' for Brianchon's theorem, too: Let coincide two neighbored tangents. Their point of intersection becomes a point of the conic. In the diagram three pairs of neighbored tangents coincide. This procedure results in a statement on [[inellipse]]s of triangles. From a projective point of view the two triangles <math>P_1P_3P_5</math> and <math>P_2P_4P_6</math> lie perspectively with center <math>B</math>. That means there exists a central collineation, which maps the one onto the other triangle. But only in special cases this collineation is an affine scaling. For example for a Steiner inellipse, where the Brianchon point is the centroid.
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