Area Ratio

Geometry Level 5

\(ABC\) is a triangle. Points \(D, E\) and \(F\) are on \(BC, CA\) and \(AB\), respectively, such that \( \frac {BD}{DC} = \frac {CE}{EA} = \frac {AF}{FB} = 2 \). Let \( AD\) and \(BE\) intersect at \(P\), \(BE\) and \(CF\) intersect at \(Q\), and \(CF\) and \(AD\) intersect at \(R\). What is the ratio \( [ABC]:[PQR] \)?

Details and assumptions

\( [PQRS]\) represents the area of the figure \(PQRS\).

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