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2019 Serbia MO Day 1 P3

Source: 2019 Serbia MO

April 7, 2019
geometry

Problem Statement

Let kk be the circle inscribed in convex quadrilateral ABCDABCD. Lines ADAD and BCBC meet at PP ,and circumcircles of △PAB\triangle PAB and △PCD\triangle PCD meet in XX . Prove that tangents from XX to kk form equal angles with lines AXAX and CXCX .
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