OMM 1997 Problem 5

Let $P,Q,R$ be points on the sides $BC,CA,AB$ respectively of a triangle $ABC$ . Suppose that $BQ$ and $CR$ meet at $A', AP$ and $CR$ meet at $B'$ , and $AP$ and $BQ$ meet at $C'$ , such that $AB' = B'C', BC' =C'A'$ , and $CA'= A'B'$ . Compute the ratio of the area of $\triangle PQR$ to the area of $\triangle ABC$ .