What name shall I give to this problem? - 2

Geometry Level 5

In \(\triangle ABC\), \(D\) and \(E\) are points on \(BC\) such that \(BD = DE = EC\). \(F\) is a point on \(AC\) such that \(AF=FC\). If \(AD\) and \(AE\) intersect \(BF\) respectively at \(P\) and \(Q\). Then, the ratio \(\dfrac{BP}{PQ}\) can be expressed as \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime integers. Find \(10a+b\).

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