IMO Shortlist 2011 problem G1
Dodao/la: arhiva23. lipnja 2013.
be an acute triangle. Let
be a circle whose centre
lies on the side
. Suppose that
is tangent to
. Suppose also that the circumcentre
lies on the shorter arc
. Prove that the circumcircle of
meet at two points.
Proposed by Härmel Nestra, Estonia
Izvor: Međunarodna matematička olimpijada, shortlist 2011