IMO Shortlist 1997 problem 25


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2. travnja 2012.
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Let X,Y,Z be the midpoints of the small arcs BC,CA,AB respectively (arcs of the circumcircle of ABC). M is an arbitrary point on BC, and the parallels through M to the internal bisectors of \angle B,\angle C cut the external bisectors of \angle C,\angle B in N,P respectively. Show that XM,YN,ZP concur.
Izvor: Međunarodna matematička olimpijada, shortlist 1997