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concurrent wanted, 4 right angles givne

Source: 2013 XVI All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p15

May 11, 2021
geometryconcurrentconcurrencyUkrainian TYM

Problem Statement

Inside the acute-angled triangle ABCABC, mark the point OO so that ∠AOB=90o\angle AOB=90^o, a point MM on the side BCBC such that ∠COM=90o\angle COM=90^o, and a point NN on the segment BOBO such that ∠OMN=90o\angle OMN = 90^o. Let PP be the point of intersection of the lines AMAM and CNCN, and let QQ be a point on the side ABAB that such ∠POQ=90o\angle POQ = 90^o. Prove that the lines AN,COAN, CO and MQMQ intersect at one point.
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