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Sharygin 2024 Correspondence P3

Source: Sharygin Correspondence Round 2024 P3

March 6, 2024
geometry

Problem Statement

Let ABCABC be an acute-angled triangle, and MM be the midpoint of the minor arc BCBC of its circumcircle. A circle ω\omega touches the side AB,ACAB, AC at points P,QP, Q respectively and passes through MM. Prove that BP+CQ=PQBP + CQ = PQ.
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