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nice problem about 2 Lemoine points, concurrent

Source: 2023 Viet Nam math olympiad for high school students D1 P9

March 20, 2023
geometry

Problem Statement

Given a quadrilateral ABCDABCD inscribed in (O)(O). Let L,JL, J be the Lemoine point of △ABC\triangle ABC and △ACD\triangle ACD.
Prove that: AC,BD,LJAC, BD, LJ are concurrent.
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