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concurent lines related to midpoints of chords and midpoints of arcs

Source: 2011 Sharygin Geometry Olympiad Correspondence Round P21

April 7, 2019
geometryChordsmidpointsarc midpointarcconcurrencyconcurrent

Problem Statement

On a circle with diameter ACAC, let BB be an arbitrary point distinct from AA and CC. Points M,NM, N are the midpoints of chords AB,BCAB, BC, and points P,QP, Q are the midpoints of smaller arcs restricted by these chords. Lines AQAQ and BCBC meet at point KK, and lines CPCP and ABAB meet at point LL. Prove that lines MQ,NPMQ, NP and KLKL concur.
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