IMO Shortlist 2012 problem G8
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Avg: 9,0 Let
be a triangle with circumcircle
and
a line without common points with
. Denote by
the foot of the perpendicular from the center of
to
. The side-lines
intersect
at the points
different from
. Prove that the circumcircles of the triangles
,
and
have a common point different from
or are mutually tangent at
.
















Izvor: Međunarodna matematička olimpijada, shortlist 2012