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 inellipses of triangles. from a projective point of view the two triangles formula_4 and formula_5 lie perspectively with center formula_3. 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.