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A "cyclic" (maybe projective) problem

Source: Problem 2, Brazilian Olympic Revenge 2005

June 1, 2005
projective geometrygeometry solvedgeometry

Problem Statement

Let Γ\Gamma be a circumference, and A,B,C,DA,B,C,D points of Γ\Gamma (in this order). rr is the tangent to Γ\Gamma at point A. ss is the tangent to Γ\Gamma at point D. Let E=r∩BC,F=s∩BCE=r \cap BC,F=s \cap BC. Let X=r∩s,Y=AF∩DE,Z=AB∩CDX=r \cap s,Y=AF \cap DE,Z=AB \cap CD Show that the points X,Y,ZX,Y,Z are collinear. Note: assume the existence of all above points.
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