CEMC Galois, 2010

Geometry Difficulty 2.0 Junior Prove it Canada

In $\triangle ABC$ , point $D$ is the midpoint of side $BC$ . Point $E$ is on $AC$ such that $AE : EC = 1 : 2$ . Point $F$ is on $AD$ such that $AF : FD = 3 : 1$ . If the area of $\triangle DEF$ is $17$ , determine the area of $\triangle ABC$ .

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