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