IMO Shortlist 2012 problem G6


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3. studenoga 2013.
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Let ABC be a triangle with circumcenter O and incenter I. The points D,E and F on the sides BC,CA and AB respectively are such that BD+BF=CA and CD+CE=AB. The circumcircles of the triangles BFD and CDE intersect at P \neq D. Prove that OP=OI.
Izvor: Međunarodna matematička olimpijada, shortlist 2012