IMO Shortlist 1969 problem 5


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2. travnja 2012.
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(BEL 5) Let G be the centroid of the triangle OAB.
(a) Prove that all conics passing through the points O,A,B,G are hyperbolas.
(b) Find the locus of the centers of these hyperbolas.
Izvor: Međunarodna matematička olimpijada, shortlist 1969