# Centroid and summed ratios

Geometry Level pending

$$PQR$$ is a triangle with its centroid at the point $$N$$ and the circumcircle of $$PQR$$ is denoted by $$L$$. The line segments $$PN$$, $$QN$$ and $$RN$$ meet $$L$$ again respectively at the points $$S$$, $$T$$ and $$U$$.

The respective lengths of the line segments $$PN$$, $$QN$$, $$RN$$, $$NS$$, $$NT$$ and $$NU$$ are denoted by $$a$$, $$b$$, $$c$$, $$d$$, $$e$$ and $$f$$.

Determine $$\dfrac{a}{d}+\dfrac{b}{e}+\dfrac{c}{f}$$.

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