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HD ,LE, BC concurrent iff EO = EC

Source: 2021 Cono Sur Shortlist G3 https://artofproblemsolving.com/community/c1088686_cono_sur_shortlist__geometry

October 31, 2022
geometryconcurrencyconcurrent

Problem Statement

Let ABCDABCD be a parallelogram with vertices in order clockwise and let EE be the intersection of its diagonals. The circle of diameter DEDE intersects the segment ADAD at LL and ECEC at HH. The circumscribed circle of LEBLEB intersects the segment BCBC at OO. Prove that the lines HDHD , LELE and BCBC are concurrent if and only if EO=ECEO = EC.
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