IMO Shortlist 2013 problem G1
Kvaliteta:
Avg: 3,0Težina:
Avg: 6,0 Let
be an acute-angled triangle with orthocenter
, and let
be a point on side
. Denote by
and
the feet of the altitudes from
and
, respectively. Denote by
the circumcircle of
, and let
be the point on
which is diametrically opposite to
. Analogously, denote by
the circumcircle of
, and let
be the point on
which is diametrically opposite to
. Prove that
,
and
are collinear.





















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