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RU-ALLRUSSIAN 1983 Problem 17

    O is a point inside the triangle ABC. a=\mathrm{a} = area OBC, b=\mathrm{b} = area OCA, c=\mathrm{c} = area OAB. Show that the vector sum aOA+bOB+cOC\mathrm{aOA} + \mathrm{bOB} + \mathrm{cOC} is zero.

    Dataset text NuminaMath olympiads. Quoted with source.

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