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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