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tangent at intersection of diagonals of a cyclic ABD parallel to a side

Source: 2006 Oral Moscow Geometry Olympiad grades 8-9 p1

October 17, 2020
geometrytangentcyclic quadrilateral

Problem Statement

The diagonals of the inscribed quadrangle ABCDABCD intersect at point KK. Prove that the tangent at point KK to the circle circumscribed around the triangle ABKABK is parallel to CDCD.
(A Zaslavsky)