## Τρίτη, 17 Οκτωβρίου 2017

### 2004 IMO Shortlist G7

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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