The collinearity of the four points K, L, M, N is an immediate consequence of the theorem of Pascal. By the tangency at A, C, G must be on the polar of N. Similarly it is on the polar of K. Thus by the reflective property of polars, K and N must be on the polar of G. The other statement on the harmonicity of the four points (LMKN)=-1 follows from the fact that the polars of M, L are respectively lines LG and MN. Later follows from the basic construction of harmonic points through quadrilaterals (see Harmonic.html ).

See the file CyclicProjective.html for the discussion of the special case of a cyclic quadrangle.

Let (c) be the conic passing through {A,B,C,D} and tangent to line AH (see for its existence/construction the file FourPtsAndTangent2.html ). According to the first part the intersection points of line-pairs (AB,CD), (AD,BC) and the tangents at opposite vertices (t

CrossRatio0.html

CrossRatioLines.html

CyclicProjective.html

FourPtsAndTangent.html

FourPtsAndTangent2.html

GoodParametrization.html

Harmonic.html

Harmonic_Bundle.html

HomographicRelation.html

Pascal.html

Pascal2.html

PascalOnTriangles.html

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