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prove PQ> AC related to intersections of lines with circumcircles

Source: Tuymaada Junior 2006 p7

May 12, 2019
geometrycircumcirclemediangeometric inequality

Problem Statement

The median BM BM of a triangle ABC ABC intersects the circumscribed circle at point K K . The circumcircle of the triangle KMC KMC intersects the segment BC BC at point P P , and the circumcircle of AMK AMK intersects the extension of BA BA at Q Q . Prove that PQ>AC PQ> AC .
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