IMO Shortlist 2000 problem G3


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2. travnja 2012.
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Let O be the circumcenter and H the orthocenter of an acute triangle ABC. Show that there exist points D, E, and F on sides BC,CA, and AB respectively such that OD + DH = OE +EH = OF +FH and the lines AD, BE, and CF are concurrent.
Izvor: Međunarodna matematička olimpijada, shortlist 2000