APMO 2012/01

[Nadim Ul Abrar]

Let $P$ be a point in the interior of a triangle $ABC$, and let $D,E,F$ be the point of intersection of the line $AP$ and the side $BC$ of the triangle, of the line $BP$ and the side $CA$, and of the line $CP$ and the side $AB$, respectively. Prove that, the area of the triangle $ABC$ must be $6$ if the area of each of the triangles $PFA$, $PDB$ and $PEC$ is $1$