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cyclic quadr. by projections of point og circumcircle of trapezoid on sides

Source: 2004 Oral Moscow Geometry Olympiad grade 10 p5

October 28, 2020
geometrycyclic quadrilateraltrapezoid

Problem Statement

Trapezoid ABCDABCD with bases ABAB and CDCD is inscribed in a circle. Prove that the quadrilateral formed by orthogonal projections of any point of this circle onto lines AC,BC,ADAC, BC, AD and BDBD is inscribed.