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Strange Geometry

Source: CSMO 2019 Grade 10 Problem 7

July 31, 2019
geometry

Problem Statement

Let ABCDABCD be a given convex quadrilateral in a plane. Prove that there exist a line with four different points P,Q,R,SP,Q,R,S on it and a square A’B’C’D’A’B’C’D’ such that PP lies on both line ABAB and A’B’,A’B’, QQ lies on both line BCBC and B’C’,B’C’, RR lies on both line CDCD and C’D’,C’D’, SS lies on both line DADA and D’A’.D’A’.
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