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AC = PQ, intersecting circumcircles (Kharkiv City X 2015 - Ukr)

Source:

March 15, 2020
geometrycircumcirclecirclesequal segmentsKharkiv

Problem Statement

On side ABAB of triangle ABCABC, point MM is selected. A straight line passing through MM intersects the segment ACAC at point NN and the ray CBCB at point KK. The circumscribed circle of the triangle AMNAMN intersects ω\omega, the circumscribed circle of the triangle ABCABC, at points AA and SS. Straight lines SMSM and SKSK intersect with ω\omega for the second time at points PP and QQ, respectively. Prove that AC=PQAC = PQ.
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