ÖMO 1983 Problem 3

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: $S_{A''B''C''}=3S_{ABC}+4S_{A'B'C'}$ .