"degenerate case of Pascal's theorem"|
Consider the degenerate case of Pascal's theorem when vertices A and B, and vertices D and E, respectively, merge. The figure from the proof given on this site degenerates into a figure inscribed in a circle. For simplicity say we have points A, B, C, and D arranged cyclically on the circle, and the six lines tA =tangent at A, AB, BC, tC =tangent at C, CD and DA. Can we somehow adapt the proof of Pascal's theorem to show that|
X = tA * tC
Y = AB * CD and
Z = BC * DA
are collinear? (* means intersection here) I am trying to construct a proof of this fact using only classical tools and there are very few tools available to prove colinearity of three points.
John A. Velling