Area Ratio

Geometry Level 5

ABCABC is a triangle. Points D,ED, E and FF are on BC,CABC, CA and ABAB, respectively, such that BDDC=CEEA=AFFB=2 \frac {BD}{DC} = \frac {CE}{EA} = \frac {AF}{FB} = 2 . Let AD AD and BEBE intersect at PP, BEBE and CFCF intersect at QQ, and CFCF and ADAD intersect at RR. What is the ratio [ABC]:[PQR] [ABC]:[PQR] ?

Details and assumptions

[PQRS] [PQRS] represents the area of the figure PQRSPQRS.

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