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locus of P such that (ABP)=(ACP)=(BCP) for given ABC

Source: Mathematics Regional Olympiad of Mexico West 2017 P4

September 8, 2022
geometryequal areas

Problem Statement

Let △ABC\vartriangle ABC be a triangle. Determine all points PP in the plane such that the triangles △ABP\vartriangle ABP, △ACP\vartriangle ACP and △BCP\vartriangle BCP all have the same area.
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