IMO Shortlist 2004 problem G7
For a given triangle
, let
be a variable point on the line
such that
lies between
and
and the incircles of the triangles
and
intersect at two distinct points
and
Prove that the line
passes through a point independent of
.
comment
An extension by Darij Grinberg can be found here.
%V0
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 $X$.
comment
An extension by Darij Grinberg can be found here.
Source: Međunarodna matematička olimpijada, shortlist 2004
Školjka 
