IMO Shortlist 2006 problem G1
Dodao/la:
arhiva2. travnja 2012. Let

be triangle with incenter

. A point

in the interior of the triangle satisfies

Show that

, and that equality holds if and only if

.
%V0
Let $ABC$ be triangle with incenter $I$. A point $P$ in the interior of the triangle satisfies $$\angle PBA+\angle PCA = \angle PBC+\angle PCB.$$ Show that $AP \geq AI$, and that equality holds if and only if $P=I$.
Izvor: Međunarodna matematička olimpijada, shortlist 2006