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locus of points P with equal triangle areas (ABP)=(CDP)

Source: 1997 Argentina OMA L3 p5

June 11, 2020
geometryLocusarea of a triangleequal areas

Problem Statement

Given two non-parallel segments ABAB and CDCD on the plane, find the locus of points PP on the plane such that the area of triangle ABPABP is equal to the area of triangle CDPCDP.