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Two Thales circles and a tangent line

Source: Baltic Way 2020, Problem 11

November 14, 2020
geometrygeometry proposed

Problem Statement

Let ABCABC be a triangle with AB>ACAB > AC. The internal angle bisector of ∠BAC\angle BAC intersects the side BCBC at DD. The circles with diameters BDBD and CDCD intersect the circumcircle of △ABC\triangle ABC a second time at P≠BP \not= B and Q≠CQ \not= C, respectively. The lines PQPQ and BCBC intersect at XX. Prove that AXAX is tangent to the circumcircle of △ABC\triangle ABC.
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