IMO Shortlist 2001 problem G2
Dodao/la:
arhiva2. travnja 2012. Consider an acute-angled triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
. Let
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
be the foot of the altitude of triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
issuing from the vertex
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
, and let
![O](/media/m/9/6/0/9601b72f603fa5d15addab9937462949.png)
be the circumcenter of triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
. Assume that
![\angle C \geq \angle B+30^{\circ}](/media/m/5/f/4/5f49fd17860fa130600f0b7288d22e72.png)
. Prove that
![\angle A+\angle COP < 90^{\circ}](/media/m/d/6/e/d6e8eb73141486e8c0784e8e77a5685c.png)
.
%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