IMO 1969 LL BEL5

Let G be the centroid of the triangle OAB.

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IMO 1969 LL BEL5

Origin: BEL

Problem

Let G be the centroid of the triangle OAB. (a) Prove that all conics passing through the points O, A, B, G are hyper- bolas. (b) Find the locus of the centers of these hyperbolas.