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cyclic quadrilateral and diagonals: OY perp. XY

Source: china

October 28, 2004
geometrycircumcirclecyclic quadrilateralgeometry solved

Problem Statement

The diagonals ACAC and BDBD of a cyclic quadrilateral ABCDABCD meet at a point XX. The circumcircles of triangles ABXABX and CDXCDX meet at a point YY (apart from XX). Let OO be the center of the circumcircle of the quadrilateral ABCDABCD. Assume that the points OO, XX, YY are all distinct. Show that OYOY is perpendicular to XYXY.
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