IMO Shortlist 2006 problem G1


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April 2, 2012
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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.
Source: Međunarodna matematička olimpijada, shortlist 2006