# 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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