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Source: Austria 1983

July 7, 2009
geometryanalytic geometrygeometry unsolved

Problem Statement

Let P P be a point in the plane of a triangle ABC ABC. Lines AP,BP,CP AP,BP,CP respectively meet lines BC,CA,AB BC,CA,AB at points A′,B′,C′ A',B',C'. Points A′′,B′′,C′′ A'',B'',C'' are symmetric to A,B,C A,B,C with respect to A′,B′,C′, A',B',C', respectively. Show that: S_{A''B''C''}\equal{}3S_{ABC}\plus{}4S_{A'B'C'}.
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