IMO Shortlist 2004 problem G7


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For a given triangle ABC, let X be a variable point on the line BC such that C lies between B and X and the incircles of the triangles ABX and ACX intersect at two distinct points P and Q. Prove that the line PQ passes through a point independent of X.

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An extension by Darij Grinberg can be found here.
Izvor: Međunarodna matematička olimpijada, shortlist 2004