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Circumcircle geometry

Source: Turkey JBMO TST 2024 P7

May 13, 2024
geometrygeometric transformationreflectioncircumcircle

Problem Statement

Let ABCDABCD be circumscribed quadrilateral such that the midpoints of ABAB,BCBC,CDCD and DADA are KK, LL, MM, NN respectively. Let the reflections of the point MM wrt the lines ADAD and BCBC be PP and QQ respectively. Let the circumcenter of the triangle KPQKPQ be RR. Prove that RN=RLRN=RL
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