On side AB of triangle ABC, point M is selected. A straight line passing through M intersects the segment AC at point N and the ray CB at point K. The circumscribed circle of the triangle AMN intersects ω, the circumscribed circle of the triangle ABC, at points A and S. Straight lines SM and SK intersect with ω for the second time at points P and Q, respectively. Prove that AC=PQ. geometrycircumcirclecirclesequal segmentsKharkiv