IMO Shortlist 2003 problem G2

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Dodao/la: arhiva
2. travnja 2012.
Given three fixed pairwisely distinct points A, B, C lying on one straight line in this order. Let G be a circle passing through A and C whose center does not lie on the line AC. The tangents to G at A and C intersect each other at a point P. The segment PB meets the circle G at Q.

Show that the point of intersection of the angle bisector of the angle AQC with the line AC does not depend on the choice of the circle G.
Izvor: Međunarodna matematička olimpijada, shortlist 2003