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Prove all conics are hyperbolas and find locus of centers.

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September 29, 2010
conicshyperbolageometrycircumcircleIMO ShortlistIMO Longlist

Problem Statement

(BEL5)(BEL 5) Let GG be the centroid of the triangle OAB.OAB. (a)(a) Prove that all conics passing through the points O,A,B,GO,A,B,G are hyperbolas. (b)(b) Find the locus of the centers of these hyperbolas.
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