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the locus of $P$

Source: Italy TST 2009 p2

March 10, 2012
geometryparameterizationgeometry unsolved

Problem Statement

ABCABC is a triangle in the plane. Find the locus of point PP for which PA,PB,PCPA,PB,PC form a triangle whose area is equal to one third of the area of triangle ABCABC.
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