In fact, by this theorem, the involution defined on line AC by the pair of points (A,C) and (F,G), F, G being the intersections of AC with t' and t respectively, has a fixed point Y on the chord joining the tangent points of t and t'.

Analogously the involution interchanging (A,B) and (H,I) on line AB has a fixed point X on the same chord. Thus, the chord XY of tangency is known and by intersecting it with t and t' we obtain two additional points D, E and reduce the problem to the one of construction of a conic passing through five points: {A,B,C,D,E}.

CrossRatio0.html

DesarquesInvolution.html

DesarquesInvolution2.html

DesarquesInvolution3.html

HomographicRelation.html

HomographicRelationExample.html

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