IMO Shortlist 2001 problem G2
Dodao/la:
arhiva2. travnja 2012. Consider an acute-angled triangle
. Let
be the foot of the altitude of triangle
issuing from the vertex
, and let
be the circumcenter of triangle
. Assume that
. Prove that
.
%V0
Consider an acute-angled triangle $ABC$. Let $P$ be the foot of the altitude of triangle $ABC$ issuing from the vertex $A$, and let $O$ be the circumcenter of triangle $ABC$. Assume that $\angle C \geq \angle B+30^{\circ}$. Prove that $\angle A+\angle COP < 90^{\circ}$.
Izvor: Međunarodna matematička olimpijada, shortlist 2001
Školjka 
