IMO Shortlist 1991 problem 4
Dodao/la:
arhiva2. travnja 2012. Let
![\,ABC\,](/media/m/8/8/4/884e479ba17d93a194ee377c6ff1cbd5.png)
be a triangle and
![\,P\,](/media/m/7/9/7/79743447988dfd17a0bf256451541cf0.png)
an interior point of
![\,ABC\,](/media/m/8/8/4/884e479ba17d93a194ee377c6ff1cbd5.png)
. Show that at least one of the angles
![\,\angle PAB,\;\angle PBC,\;\angle PCA\,](/media/m/e/a/5/ea58e99d2313f268b8407a868baada1e.png)
is less than or equal to
![30^{\circ }](/media/m/4/0/d/40da2c57b78b6d00927c0094ae890365.png)
.
%V0
Let $\,ABC\,$ be a triangle and $\,P\,$ an interior point of $\,ABC\,$. Show that at least one of the angles $\,\angle PAB,\;\angle PBC,\;\angle PCA\,$ is less than or equal to $30^{\circ }$.
Izvor: Međunarodna matematička olimpijada, shortlist 1991